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  • Bounds on regularity of quadratic monomial ideals
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-07-15
    Grigoriy Blekherman; Jaewoo Jung

    Castelnuovo-Mumford regularity is a measure of algebraic complexity of an ideal. Regularity of monomial ideals can be investigated combinatorially. We use a simple graph decomposition and results from structural graph theory to prove, improve and generalize many of the known bounds on regularity of quadratic square-free monomial ideals.

    更新日期:2020-07-15
  • On split graphs with three or four distinct (normalized) Laplacian eigenvalues
    J. Comb. Des. (IF 0.731) Pub Date : 2020-07-13
    Shuchao Li; Wanting Sun

    It is well known to us that a graph of diameter l has at least l + 1 eigenvalues. A graph is said to be Laplacian (resp, normalized Laplacian ) l ‐extremal if it is of diameter l having exactly l + 1 distinct Laplacian (resp, normalized Laplacian) eigenvalues. A graph is split if its vertex set can be partitioned into a clique and a stable set. Each split graph is of diameter at most 3. In this paper

    更新日期:2020-07-14
  • The pseudoforest analogue for the Strong Nine Dragon Tree Conjecture is true
    J. Comb. Theory B (IF 1.306) Pub Date : 2020-07-14
    Logan Grout; Benjamin Moore

    We prove that for any positive integers k and d, if a graph G has maximum average degree at most 2k+2dd+k+1, then G decomposes into k+1 pseudoforests C1,…,Ck+1 so that for at least one of the pseudoforests, each connected component has at most d edges.

    更新日期:2020-07-14
  • The construction of multipermutation solutions of the Yang-Baxter equation of level 2
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-07-13
    Přemysl Jedlička; Agata Pilitowska; Anna Zamojska-Dzienio

    We study involutive set-theoretic solutions of the Yang-Baxter equation of multipermutation level 2. These solutions happen to fall into two classes – distributive ones and non-distributive ones. The distributive ones can be effectively constructed using a set of abelian groups and a matrix of constants. Using this construction, we enumerate all distributive involutive solutions up to size 14. The

    更新日期:2020-07-13
  • Joint optimal pricing and advertising policies in a fashion supply chain under the ODM strategy considering fashion level and goodwill
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-07-13
    Qi Chen, Qi Xu

    The original design manufacturing (ODM) strategy has become popular in the fashion supply chain field. We consider apparel’s fashion level and advertising effort as important influential factors on goodwill, and present a differential game involving a fashion brand and a supplier. The supplier controls the design improvement effort applied to the apparel and sells it to end consumers through the fashion

    更新日期:2020-07-13
  • Properties of a q -Analogue of Zero Forcing
    Graphs Comb. (IF 0.597) Pub Date : 2020-07-13
    Steve Butler, Craig Erickson, Shaun Fallat, H. Tracy Hall, Brenda Kroschel, Jephian C.-H. Lin, Bryan Shader, Nathan Warnberg, Boting Yang

    Zero forcing is a combinatorial game played on a graph where the goal is to start with all vertices unfilled and to change them to filled at minimal cost. In the original variation of the game there were two options. Namely, to fill any one single vertex at the cost of a single token; or if any currently filled vertex has a unique non-filled neighbor, then the neighbor is filled for free. This paper

    更新日期:2020-07-13
  • Separability of Schur Rings Over Abelian Groups of Odd Order
    Graphs Comb. (IF 0.597) Pub Date : 2020-07-09
    Grigory Ryabov

    An S-ring (a Schur ring) is said to be separable with respect to a class of groups \({\mathcal {K}}\) if every algebraic isomorphism from the S-ring in question to an S-ring over a group from \({\mathcal {K}}\) is induced by a combinatorial isomorphism. A finite group G is said to be separable with respect to \({\mathcal {K}}\) if every S-ring over G is separable with respect to \({\mathcal {K}}\)

    更新日期:2020-07-10
  • Probabilistic existence of large sets of designs
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-07-08
    Shachar Lovett; Sankeerth Rao; Alexander Vardy

    A new probabilistic technique for establishing the existence of certain regular combinatorial structures has been introduced by Kuperberg, Lovett, and Peled (STOC 2012). Using this technique, it can be shown that under certain conditions, a randomly chosen structure has the required properties of a t-(n,k,λ) combinatorial design with tiny, yet positive, probability. The proof method of KLP is adapted

    更新日期:2020-07-08
  • Combinatorial designs for deep learning
    J. Comb. Des. (IF 0.731) Pub Date : 2020-05-04
    Shoko Chisaki; Ryoh Fuji‐Hara; Nobuko Miyamoto

    Deep learning is a machine learning methodology using a multilayer neural network. Let V 1 , V 2 , … , V L be mutually disjoint node sets (layers). A multilayer neural network can be regarded as a union of the complete bipartite graphs K ∣ V i ∣ , ∣ V i + 1 ∣ on consecutive two node sets V i and V i + 1 for i = 1 , 2 , … , L − 1 . The edges of a bipartite graph function as weights which are represented

    更新日期:2020-07-07
  • Deza graphs with parameters (v,k,k−2,a)
    J. Comb. Des. (IF 0.731) Pub Date : 2020-05-03
    Vladislav V. Kabanov; Leonid Shalaginov

    A Deza graph with parameters ( v , k , b , a ) is a k ‐regular graph on v vertices in which the number of common neighbors of two distinct vertices takes one of the following values: b or a , where b ≥ a . In the previous papers Deza graphs with b = k − 1 were characterized. In this paper, we characterize Deza graphs with b = k − 2 .

    更新日期:2020-07-07
  • Exceptions and characterization results for type‐1 λ‐designs
    J. Comb. Des. (IF 0.731) Pub Date : 2020-05-18
    Ajeet Kumar Yadav; Rajendra M. Pawale; Mohan S. Shrikhande

    Let X be a finite set with v elements, called points and β be a family of subsets of X , called blocks. A pair ( X , β ) is called λ ‐design whenever ∣ β ∣ = ∣ X ∣ and 1. for all B i , B j ∈ β , i ≠ j , ∣ B i ∩ B j ∣ = λ ; 2. for all B j ∈ β , ∣ B j ∣ = k j > λ , and not all k j are equal. The only known examples of λ ‐designs are so‐called type‐1 designs, which are obtained from symmetric designs

    更新日期:2020-07-07
  • Symmetric designs and projective special linear groups of dimension at most four
    J. Comb. Des. (IF 0.731) Pub Date : 2020-06-07
    Seyed Hassan Alavi; Mohsen Bayat; Asharf Daneshkhah

    In this article, we study symmetric ( v , k , λ ) designs admitting a flag‐transitive and point‐primitive automorphism group G whose socle is isomorphic to a projective special linear group of dimension at most four. We, in particular, determine all such possible parameters ( v , k , λ ) and show that such a design belongs to one of two infinite families of point‐hyperplane designs or it is isomorphic

    更新日期:2020-07-07
  • The (theta, wheel)-free graphs Part IV: Induced paths and cycles
    J. Comb. Theory B (IF 1.306) Pub Date : 2020-07-07
    Marko Radovanović; Nicolas Trotignon; Kristina Vušković

    A hole in a graph is a chordless cycle of length at least 4. A theta is a graph formed by three internally vertex-disjoint paths of length at least 2 between the same pair of distinct vertices. A wheel is a graph formed by a hole and a node that has at least 3 neighbors in the hole. In this series of papers we study the class of graphs that do not contain as an induced subgraph a theta nor a wheel

    更新日期:2020-07-07
  • Shortest paths among transient obstacles
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-07-07
    Anil Maheshwari, Arash Nouri, Jörg-Rüdiger Sack

    We present an optimal algorithm for determining a time-minimal rectilinear path among transient rectilinear obstacles. An obstacle is transient if it exists only for a specific time interval, i.e., it appears and then disappears at specific times. Given a point robot moving with bounded speed among non-intersecting transient rectilinear obstacles and a pair of points (s, d), we determine a time-minimal

    更新日期:2020-07-07
  • Personalized manufacturing service composition recommendation: combining combinatorial optimization and collaborative filtering
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-07-06
    Shuangyao Zhao, Qiang Zhang, Zhanglin Peng, Xiaonong Lu

    Owing to the rapid proliferation of service technologies in cross-enterprise manufacturing collaborations, manufacturing service composition (MSC) has attracted much attention from both academia and industries. However, the existing service composition is often constructed by the combination of off-line and on-line services, quality of service (QoS) attributes are not appropriate for satisfying the

    更新日期:2020-07-07
  • Eco-friendly container transshipment route scheduling problem with repacking operations
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-07-03
    Ming Liu, Rongfan Liu, E Zhang, Chengbin Chu

    Currently, a huge amount of cargo is transported via containers by liner shipping companies. Under stochastic demand, repacking operations and carbon reduction, which may lead to an increase in effectiveness and environmental improvement, have been rarely considered in previous literature. In this paper, we investigate a container transshipment route scheduling problem with repacking operations under

    更新日期:2020-07-03
  • Three-coloring triangle-free graphs on surfaces III. Graphs of girth five
    J. Comb. Theory B (IF 1.306) Pub Date : 2020-07-02
    Zdeněk Dvořák; Daniel Král'; Robin Thomas

    We show that the size of a 4-critical graph of girth at least five is bounded by a linear function of its genus. This strengthens the previous bound on the size of such graphs given by Thomassen. It also serves as the basic case for the description of the structure of 4-critical triangle-free graphs embedded in a fixed surface, presented in a future paper of this series.

    更新日期:2020-07-02
  • Maker-breaker percolation games II: Escaping to infinity
    J. Comb. Theory B (IF 1.306) Pub Date : 2020-07-02
    A. Nicholas Day; Victor Falgas–Ravry

    Let Λ be an infinite connected graph, and let v0 be a vertex of Λ. We consider the following positional game. Two players, Maker and Breaker, play in alternating turns. Initially all edges of Λ are marked as unsafe. On each of her turns, Maker marks p unsafe edges as safe, while on each of his turns Breaker takes q unsafe edges and deletes them from the graph. Breaker wins if at any time in the game

    更新日期:2020-07-02
  • Tree series and pattern avoidance in syntax trees
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-07-02
    Samuele Giraudo

    A syntax tree is a planar rooted tree where internal nodes are labeled on a graded set of generators. There is a natural notion of occurrence of contiguous pattern in such trees. We describe a way, given a set of generators G and a set of patterns P, to enumerate the trees constructed on G and avoiding P. The method is built around inclusion-exclusion formulas forming a system of equations on formal

    更新日期:2020-07-02
  • Extremal Graphs for Blow-Ups of Keyrings
    Graphs Comb. (IF 0.597) Pub Date : 2020-07-01
    Zhenyu Ni, Liying Kang, Erfang Shan, Hui Zhu

    The blow-up of a graph H is the graph obtained from replacing each edge in H by a clique of the same size where the new vertices of the cliques are all different. Given a graph H and a positive integer n, the extremal number, ex(n, H), is the maximum number of edges in a graph on n vertices that does not contain H as a subgraph. A keyring \(C_s(k)\) is a \((k+s)\)-edge graph obtained from a cycle of

    更新日期:2020-07-01
  • Induced equators in flag spheres
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-06-30
    Maria Chudnovsky; Eran Nevo

    We propose a combinatorial approach to the following strengthening of Gal's conjecture: γ(Δ)≥γ(E) coefficientwise, where Δ is a flag homology sphere and E⊆Δ an induced homology sphere of codimension 1. We provide partial evidence in favor of this approach, and prove a nontrivial nonlinear inequality that follows from the above conjecture, for boundary complexes of flag d-polytopes: h1(Δ)hi(Δ)≥(d−i

    更新日期:2020-06-30
  • Computing the k-binomial complexity of the Thue–Morse word
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-06-30
    Marie Lejeune; Julien Leroy; Michel Rigo

    Two words are k-binomially equivalent whenever they share the same subwords, i.e., subsequences, of length at most k with the same multiplicities. This is a refinement of both the abelian equivalence and the Simon congruence. The k-binomial complexity of an infinite word x maps the integer n to the number of classes in the quotient, by this k-binomial equivalence relation, of the set of factors of

    更新日期:2020-06-30
  • A general framework for path convexities
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-06-29
    João Vinicius C. Thompson, Loana T. Nogueira, Fábio Protti, Raquel S. F. Bravo, Mitre C. Dourado, Uéverton S. Souza

    In this work we deal with the so-called path convexities, defined over special collections of paths. For example, the collection of the shortest paths in a graph is associated with the well-known geodesic convexity, while the collection of the induced paths is associated with the monophonic convexity; and there are many other examples. Besides reviewing the path convexities in the literature, we propose

    更新日期:2020-06-29
  • Maximum weight induced matching in some subclasses of bipartite graphs
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-06-28
    B. S. Panda, Arti Pandey, Juhi Chaudhary, Piyush Dane, Manav Kashyap

    A subset \(M\subseteq E\) of edges of a graph \(G=(V,E)\) is called a matching in G if no two edges in M share a common vertex. A matching M in G is called an induced matching if G[M], the subgraph of G induced by M, is the same as G[S], the subgraph of G induced by \(S=\{v \in V |\)v is incident on an edge of \(M\}\). The Maximum Induced Matching problem is to find an induced matching of maximum cardinality

    更新日期:2020-06-28
  • The multicolour size-Ramsey number of powers of paths
    J. Comb. Theory B (IF 1.306) Pub Date : 2020-06-27
    Jie Han; Matthew Jenssen; Yoshiharu Kohayakawa; Guilherme Oliveira Mota; Barnaby Roberts

    Given a positive integer s, a graph G is s-Ramsey for a graph H, denoted G→(H)s, if every s-colouring of the edges of G contains a monochromatic copy of H. The s-colour size-Ramsey number rˆs(H) of a graph H is defined to be rˆs(H)=min⁡{|E(G)|:G→(H)s}. We prove that, for all positive integers k and s, we have rˆs(Pnk)=O(n), where Pnk is the kth power of the n-vertex path Pn.

    更新日期:2020-06-27
  • Online pickup and delivery problem with constrained capacity to minimize latency
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-06-27
    Haiyan Yu, Xianwei Luo, Tengyu Wu

    The online pickup and delivery problem is motivated by the takeaway order delivery on crowdsourcing delivery platform, which is a newly emerged online to offline business model based on sharing economy. Considering the features of crowdsourcing delivery, an online pickup and delivery problem with constrained capacity is proposed, whose objective is to route a delivery man with constrained capacity

    更新日期:2020-06-27
  • Average eccentricity, minimum degree and maximum degree in graphs
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-06-26
    P. Dankelmann, F. J. Osaye

    Let G be a connected finite graph with vertex set V(G). The eccentricity e(v) of a vertex v is the distance from v to a vertex farthest from v. The average eccentricity of G is defined as \(\frac{1}{|V(G)|}\sum _{v \in V(G)}e(v)\). We show that the average eccentricity of a connected graph of order n, minimum degree \(\delta \) and maximum degree \(\Delta \) does not exceed \(\frac{9}{4} \frac{n-\Delta

    更新日期:2020-06-26
  • Reconfiguration of garbage collection system based on Voronoi graph theory: a simulation case of Beijing region
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-06-25
    Chun-lin Xin, Shuo Liang, Feng-wu Shen

    With urban development, many small urban areas are being integrated into large ones, which leads to redundancy of domestic waste disposal facilities. How to optimize these facilities is a major problem of urban administrative departments. In this study, we consider three strategies to deal with this problem, which are redundant deletion, garbage bin redistribution, and system reconstruction, through

    更新日期:2020-06-26
  • Affine Mendelsohn triple systems and the Eisenstein integers
    J. Comb. Des. (IF 0.731) Pub Date : 2020-06-24
    Alex W. Nowak

    We define a Mendelsohn triple system (MTS) of order coprime with 3, and having multiplication affine over an abelian group, to be affine, nonramified . By exhibiting a one‐to‐one correspondence between isomorphism classes of affine MTS and those of modules over the Eisenstein integers, we solve the isomorphism problem for affine, nonramified MTS and enumerate these isomorphism classes (extending the

    更新日期:2020-06-25
  • Mutation of type D friezes
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-06-25
    A. Garcia Elsener; K. Serhiyenko

    In this article we study mutation of friezes of type D. We provide a combinatorial formula for the entries in a frieze after mutation. The two main ingredients in the proof include a certain transformation of a type D frieze into a sub-pattern of a frieze of type A and the mutation formula for type A friezes recently found by Baur et al.

    更新日期:2020-06-25
  • The principal eigenvector to $$\alpha $$α -spectral radius of hypergraphs
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-06-25
    Jing Wang, Liying Kang, Erfang Shan

    For a connected hypergraph H with \(rank(H)=r\) , let \(\mathcal {D}(H)\) and \(\mathcal {A}(H)\) be the diagonal tensor of degrees and the adjacency tensor of H, respectively. For \(0 \le \alpha < 1\), the \(\alpha \)-spectral radius \(\rho _{\alpha }(H)\) of H is defined as \(\rho _{\alpha }(H)=\max \{x^{T}(\mathcal {A}_{\alpha }x)|x \in \mathbf {R}_{+}^{n},\Vert x\Vert _{r}=1\}\), where \(\mathcal

    更新日期:2020-06-25
  • Approximation algorithms for two variants of correlation clustering problem
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-06-24
    Sai Ji, Dachuan Xu, Min Li, Yishui Wang

    Correlation clustering problem is a clustering problem which has many applications such as protein interaction networks, cross-lingual link detection, communication networks, and social computing. In this paper, we introduce two variants of correlation clustering problem: correlation clustering problem on uncertain graphs and correlation clustering problem with non-uniform hard constrained cluster

    更新日期:2020-06-25
  • A note on 3‐partite graphs without 4‐cycles
    J. Comb. Des. (IF 0.731) Pub Date : 2020-06-22
    Zequn Lv; Mei Lu; Chunqiu Fang

    Let C 4 be a cycle of order 4. Write e x ( n , n , n , C 4 ) for the maximum number of edges in a balanced 3‐partite graph whose vertex set consists of three parts, each has n vertices that have no subgraph isomorphic to C 4 . In this paper, we show that e x ( n , n , n , C 4 ) ≥ 3 2 n ( p + 1 ) , where n = p ( p − 1 ) 2 and p is a prime number. Note that e x ( n , n , n , C 4 ) ≤ ( 3 2 2 + o ( 1 )

    更新日期:2020-06-23
  • Ternary codes, biplanes, and the nonexistence of some quasisymmetric and quasi‐3 designs
    J. Comb. Des. (IF 0.731) Pub Date : 2020-06-22
    Akihiro Munemasa; Vladimir D. Tonchev

    The dual codes of the ternary linear codes of the residual designs of biplanes on 56 points are used to prove the nonexistence of quasisymmetric 2‐ ( 56 , 12 , 9 ) and 2‐ ( 57 , 12 , 11 ) designs with intersection numbers 0 and 3, and the nonexistence of a 2‐ ( 267 , 57 , 12 ) quasi‐3 design. The nonexistence of a 2‐ ( 149 , 37 , 9 ) quasi‐3 design is also proved.

    更新日期:2020-06-23
  • An asymptotic resolution of a problem of Plesník
    J. Comb. Theory B (IF 1.306) Pub Date : 2020-06-22
    Stijn Cambie

    Fix d≥3. We show the existence of a constant c>0 such that any graph of diameter at most d has average distance at most d−cd3/2n, where n is the number of vertices. Moreover, we exhibit graphs certifying sharpness of this bound up to the choice of c. This constitutes an asymptotic solution to a longstanding open problem of Plesník. Furthermore we solve the problem exactly for digraphs if the order

    更新日期:2020-06-23
  • Integer linear programming formulations of the filter partitioning minimization problem
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-06-21
    Hazhar Rahmani, Jason M. O’Kane

    Combinatorial filters, which take the form of labelled transition graphs, are a general representation for filtering and inference tasks in robotics. They are of particular interest in contexts where the objective is to minimize the computational resources needed to execute the filter. One specific problem is called the filter minimization (FM) problem, in which the goal is to find, for a given original

    更新日期:2020-06-22
  • A multi-period ambulance location and allocation problem in the disaster
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-06-20
    Jian Wang, Yin Wang, Mingzhu Yu

    To achieve quick response in the disaster, this paper addresses the issue of ambulance location and allocation, as well as the location problem of temporary medical centers. Considering budget and capacity limitations, a multi-period mixed integer programming model is proposed and two hybrid heuristic algorithms are designed to solve this complex problem. The proposed model and algorithm are further

    更新日期:2020-06-22
  • A multi-objective simulated annealing to solve an identical parallel machine scheduling problem with deterioration effect and resources consumption constraints
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-06-20
    Norelhouda Sekkal, Fayçal Belkaid

    Production systems are subject to machine deterioration and resource consumption constraints. The deterioration increases the processing time which leads to an increase in resource consumption. In this study, we investigate and model the behavior of a parallel machine scheduling problem with respect to the processing time. The machine is subject to deterioration and includes two resource consumption

    更新日期:2020-06-22
  • Circular Zero-Sum r -Flows of Regular Graphs
    Graphs Comb. (IF 0.597) Pub Date : 2020-04-11
    Saieed Akbari, Amir Hossein Ghodrati, Mohammad Ali Nematollahi

    A circular zero-sum flow for a graph G is a function \(f:E(G) \rightarrow {\mathbb {R}}{\setminus }\{0\}\) such that for every vertex v, \(\sum _{e\in E_v}f(e)=0\), where \(E_v\) is the set of all edges incident with v. If for each edge e, \(1\le |f(e)| \le r-1\), where \(r\ge 2\) is a real number, then f is called a circular zero-sum r-flow. Also, if r is a positive integer and for each edge e, f(e)

    更新日期:2020-06-19
  • p -Adic Roots of Chromatic Polynomials
    Graphs Comb. (IF 0.597) Pub Date : 2020-04-27
    Paul Buckingham

    The complex roots of the chromatic polynomial \(P_{G}(x)\) of a graph G have been well studied, but the p-adic roots have received no attention as yet. We consider these roots, specifically the roots in the ring \(\mathbb{Z}_p\) of p-adic integers. We first describe how the existence of p-adic roots is related to the p-divisibility of the number of colourings of a graph—colourings by at most k colours

    更新日期:2020-06-19
  • Packing and Covering Directed Triangles
    Graphs Comb. (IF 0.597) Pub Date : 2020-04-11
    Jessica McDonald, Gregory J. Puleo, Craig Tennenhouse

    We prove that if a directed multigraph D has at most t pairwise arc-disjoint directed triangles, then there exists a set of less than 2t arcs in D which meets all directed triangles in D, except in the trivial case \(t=0\). This answers affirmatively a question of Tuza from 1990.

    更新日期:2020-06-19
  • Degree Sequence Conditions for Maximally Edge-Connected and Super Edge-Connected Hypergraphs
    Graphs Comb. (IF 0.597) Pub Date : 2020-04-11
    Shuang Zhao, Yingzhi Tian, Jixiang Meng

    Let H be a connected hypergraph with minimum degree \(\delta\) and edge-connectivity \(\lambda\). The hypergraph H is maximally edge-connected if \(\lambda = \delta\), and it is super edge-connected or super-\(\lambda\), if every minimum edge-cut consists of edges incident with some vertex. There are several degree sequence conditions, for example, Goldsmith and White (Discrete Math 23: 31–36, 1978)

    更新日期:2020-06-19
  • Harmonic Index t -Designs in the Hamming Scheme for Arbitrary q
    Graphs Comb. (IF 0.597) Pub Date : 2020-04-11
    Makoto Tagami, Ryota Hori

    The notion of T-design in a symmetric association scheme was introduced by Delsarte. A harmonic index t-design is the particular case in which the index set T consists of a single index \(\{t\}\). Zhu et al. studied a harmonic index t-design in the binary Hamming scheme and gave a Fisher type lower bound on the cardinality. Also they defined the notion of a tight harmonic index design using the bound

    更新日期:2020-06-19
  • Parameterized algorithms and complexity for the traveling purchaser problem and its variants
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-06-17
    Mingyu Xiao, Jianan Zhang, Weibo Lin

    The traveling purchaser problem (TPP), a generalization of the traveling salesman problem, is to determine a tour of suppliers and purchase needed products from suppliers while minimizing the traveling and purchasing cost. This problem finds applications in the routing and scheduling contexts and its variants with different constraints have been widely studied. Motivated by the phenomenon that most

    更新日期:2020-06-18
  • More on limited packings in graphs
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-06-15
    Xuqing Bai, Hong Chang, Xueliang Li

    A set B of vertices in a graph G is called a k-limited packing if for each vertex v of G, its closed neighbourhood has at most k vertices in B. The k-limited packing number of a graph G, denoted by \(L_k(G)\), is the largest number of vertices in a k-limited packing in G. The concept of the k-limited packing of a graph was introduced by Gallant et al., which is a generalization of the well-known packing

    更新日期:2020-06-18
  • Contact graphs of ball packings
    J. Comb. Theory B (IF 1.306) Pub Date : 2020-06-17
    Alexey Glazyrin

    A contact graph of a packing of closed balls is a graph with balls as vertices and pairs of tangent balls as edges. We prove that the average degree of the contact graph of a packing of balls (with possibly different radii) in R3 is not greater than 13.92. We also find new upper bounds for the average degree of contact graphs in R4 and R5.

    更新日期:2020-06-17
  • Circular flows via extended Tutte orientations
    J. Comb. Theory B (IF 1.306) Pub Date : 2020-06-16
    Jiaao Li; Yezhou Wu; Cun-Quan Zhang

    This paper consists of two major parts. In the first part, the relations between Tutte orientations and circular flows are explored. Tutte orientation (modulo orientation) was first observed by Tutte for the study of 3-flow problem, and later extended by Jaeger for circular (2+1/p)-flows. In this paper, it is extended for circular λ-flows for all rational numbers λ. This theorem is one of the key tools

    更新日期:2020-06-16
  • Affirmative Solutions on Local Antimagic Chromatic Number
    Graphs Comb. (IF 0.597) Pub Date : 2020-06-16
    Gee-Choon Lau, Ho-Kuen Ng, Wai-Chee Shiu

    An edge labeling of a connected graph \(G = (V, E)\) is said to be local antimagic if it is a bijection \(f:E \rightarrow \{1,\ldots ,|E|\}\) such that for any pair of adjacent vertices x and y, \(f^+(x)\not = f^+(y)\), where the induced vertex label \(f^+(x)= \sum f(e)\), with e ranging over all the edges incident to x. The local antimagic chromatic number of G, denoted by \(\chi _{la}(G)\), is the

    更新日期:2020-06-16
  • A rapid learning automata-based approach for generalized minimum spanning tree problem
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-06-13
    Masoumeh Zojaji, Mohammad Reza Mollakhalili Meybodi, Kamal Mirzaie

    Generalized minimum spanning tree problem, which has several real-world applications like telecommunication network designing, is related to combinatorial optimization problems. This problem belongs to the NP-hard class and is a minimum tree on a clustered graph spanning one node from each cluster. Although exact and metaheuristic algorithms have been applied to solve the problems successfully, obtaining

    更新日期:2020-06-13
  • Multi-color Forcing in Graphs
    Graphs Comb. (IF 0.597) Pub Date : 2020-06-13
    Chassidy Bozeman, Pamela E. Harris, Neel Jain, Ben Young, Teresa Yu

    Let \(G=(V,E)\) be a finite connected graph along with a coloring of the vertices of G using the colors in a given set X. In this paper, we introduce multi-color forcing, a generalization of zero-forcing on graphs, and give conditions in which the multi-color forcing process terminates regardless of the number of colors used. We give an upper bound on the number of steps required to terminate a forcing

    更新日期:2020-06-13
  • Crossing minimization in perturbed drawings
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-06-12
    Radoslav Fulek, Csaba D. Tóth

    Due to data compression or low resolution, nearby vertices and edges of a graph drawn in the plane may be bundled to a common node or arc. We model such a “compromised” drawing by a piecewise linear map \(\varphi :G\rightarrow {\mathbb {R}}^2\). We wish to perturb \(\varphi \) by an arbitrarily small \(\varepsilon >0\) into a proper drawing (in which the vertices are distinct points, any two edges

    更新日期:2020-06-12
  • Shortest Directed Networks in the Plane
    Graphs Comb. (IF 0.597) Pub Date : 2020-06-12
    Alastair Maxwell, Konrad J. Swanepoel

    Given a set of sources and a set of sinks as points in the Euclidean plane, a directed network is a directed graph drawn in the plane with a directed path from each source to each sink. Such a network may contain nodes other than the given sources and sinks, called Steiner points. We characterize the local structure of the Steiner points in all shortest-length directed networks in the Euclidean plane

    更新日期:2020-06-12
  • Optimal Domination Polynomials
    Graphs Comb. (IF 0.597) Pub Date : 2020-06-12
    Iain Beaton, Jason I. Brown, Danielle Cox

    Let G be a graph on n vertices and m edges and D(G, x) the domination polynomial of G. In this paper we completely characterize the values of n and m for which optimal graphs exist for domination polynomials. We also show that there does not always exist least optimal graphs for the domination polynomial. Applications to network reliability are highlighted.

    更新日期:2020-06-12
  • Online economic ordering problem for deteriorating items with limited price information
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-06-11
    Wenqiang Dai, Meng Zheng, Xu Chen, Zhuolin Yang

    Traditional economic ordering model for deteriorating items assume the procurer have full information about the procurement price. In this paper, we study an online economic ordering problem for constant deteriorating rate items with limited price information under relative performance criterion of the competitive ratio (CR). We provide a simply procurement strategy as well as the optimal ordering

    更新日期:2020-06-11
  • Selfish colorful bin packing games
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-06-11
    Vittorio Bilò, Francesco Cellinese, Giovanna Melideo, Gianpiero Monaco

    We consider selfish colorful bin packing games in which a set of items, each one controlled by a selfish player, are to be packed into a minimum number of unit capacity bins. Each item has one of \(m\ge 2\) colors and no items of the same color may be adjacent in a bin. All bins have the same unitary cost which is shared among the items it contains, so that players are interested in selecting a bin

    更新日期:2020-06-11
  • Approximation algorithms for the selling with preference
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-06-11
    Pan Li, Qiang Hua, Zhijun Hu, Hing-Fung Ting, Yong Zhang

    We consider the market mechanism to sell two types of products, A and B, to a set of buyers \(I=\{1, 2, \ldots , n\}\). The amounts of products are \(m_A\) and \(m_B\) respectively. Each buyer i has his information including the budget, the preference and the utility function. On collecting the information from all buyers, the market maker determines the price of each product and allocates some amount

    更新日期:2020-06-11
  • A family of hemisystems on the parabolic quadrics
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-06-10
    Jesse Lansdown; Alice C. Niemeyer

    We construct a family of hemisystems of the parabolic quadric Q(2d,q), for all ranks d⩾2 and all odd prime powers q, that admit Ω3(q)≅PSL2(q). This yields the first known construction for d⩾4.

    更新日期:2020-06-10
  • Coordination mechanisms for scheduling selfish jobs with favorite machines
    J. Comb. Optim. (IF 0.843) Pub Date : 2020-06-10
    Cong Chen, Yinfeng Xu

    This paper studies the favorite machine model, where each machine has different speed for different types of jobs. The model is a natural generalization of the two related machines model and captures the features of some real life problems, such as the CPU–GPU task scheduling, the two products scheduling and the cloud computing task scheduling. We are interested in the game-theoretic version of the

    更新日期:2020-06-10
  • Edge-transitive bi-Cayley graphs
    J. Comb. Theory B (IF 1.306) Pub Date : 2020-06-09
    Marston Conder; Jin-Xin Zhou; Yan-Quan Feng; Mi-Mi Zhang

    A graph Γ admitting a group H of automorphisms acting semi-regularly on the vertices with exactly two orbits is called a bi-Cayley graph over H. This generalisation of a Cayley graph gives a class of graphs that includes many important examples such as the Petersen graph, the Gray graph and the Hoffman-Singleton graph. A bi-Cayley graph Γ over a group H is called normal if H is normal in the full automorphism

    更新日期:2020-06-09
  • Cycles of length three and four in tournaments
    J. Comb. Theory A (IF 1.133) Pub Date : 2020-06-09
    Timothy F.N. Chan; Andrzej Grzesik; Daniel Král'; Jonathan A. Noel

    Linial and Morgenstern conjectured that, among all n-vertex tournaments with d(n3) cycles of length three, the number of cycles of length four is asymptotically minimized by a random blow-up of a transitive tournament with all but one part of equal size and one smaller part. We prove the conjecture for d≥1/36 by analyzing the possible spectrum of adjacency matrices of tournaments. We also demonstrate

    更新日期:2020-06-09
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