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The square of every subcubic planar graph of girth at least 6 is 7-choosable Discret. Math. (IF 0.8) Pub Date : 2024-03-14 Seog-Jin Kim, Xiaopan Lian
The square of a graph , denoted , has the same vertex set as and has an edge between two vertices if the distance between them in is at most 2. Thomassen and Hartke, Jahanbekam and Thomas proved that if is a subcubic planar graph. A natural question is whether or not if is a subcubic planar graph. It was showed in that if is a subcubic planar graph of girth at least 7. We prove that if is a subcubic
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Visible lattice points along curves in higher dimensional random walks Discret. Math. (IF 0.8) Pub Date : 2024-03-14 Meijie Lu
Let be an integer, and with and , this paper concerns the generalized visibility of lattice points visited by an -random walk in . Specifically, for with , we focus on the lattice points in the walk which are -visible from a set of watch-points, and we show that, almost surely, the proportion of -visible steps is , where runs over all primes and . This paper generalizes our previous work for the visible
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On the zero-sum subsequences of modular restricted lengths Discret. Math. (IF 0.8) Pub Date : 2024-03-13 Siao Hong, Kevin Zhao
Let be an additive finite abelian group and let be a positive integer. Denote by the smallest positive integer such that every sequence over of length has a nonempty zero-sum subsequence with length . Let denote the smallest positive integer such that every sequence over of length has two nonempty zero-sum subsequences of distinct lengths. Gao et al. proved that . In this paper, we continue to investigate
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Equitable coloring of planar graphs with maximum degree at least eight Discret. Math. (IF 0.8) Pub Date : 2024-03-13 Alexandr Kostochka, Duo Lin, Zimu Xiang
The Chen-Lih-Wu Conjecture states that each connected graph with maximum degree that is not the complete graph or the complete bipartite graph admits an equitable coloring with Δ colors. For planar graphs, the conjecture has been confirmed for by Yap and Zhang and for by Nakprasit. In this paper, we present a proof that confirms the conjecture for graphs embeddable into a surface with non-negative
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Rainbow spanning trees in random subgraphs of dense regular graphs Discret. Math. (IF 0.8) Pub Date : 2024-03-12 Peter Bradshaw
We consider the following random model for edge-colored graphs. A graph on vertices is fixed, and a random subgraph is chosen by letting each edge of remain independently with probability . Then, each edge of is colored uniformly at random from the set . A result of Frieze and McKay (Random Structures and Algorithms, 1994) implies that if , , and , then almost surely contains a rainbow spanning tree
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The connection of the acyclic disconnection and feedback arc sets – On an open problem of Figueroa et al. Discret. Math. (IF 0.8) Pub Date : 2024-03-12 Laura Vargas Koch, Lukas Vogl
We examine the connection of two graph parameters, the size of a minimum feedback arcs set and the acyclic disconnection. A feedback arc set of a directed graph is a subset of arcs such that after deletion the graph becomes acyclic. The acyclic disconnection denotes the maximum number of colors that can be used in a vertex coloring such that after deletion of the monochromatic arcs the graph is acyclic
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The determinant of the Laplacian matrix of a quaternion unit gain graph Discret. Math. (IF 0.8) Pub Date : 2024-03-12 Ivan I. Kyrchei, Eran Treister, Volodymyr O. Pelykh
A quaternion unit gain graph is a graph where each orientation of an edge is given a quaternion unit, and the opposite orientation is assigned the inverse of this quaternion unit. In this paper, we provide a combinatorial description of the determinant of the Laplacian matrix of a quaternion unit gain graph by using row-column noncommutative determinants recently introduced by one of the authors. A
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The problem of path decomposition for graphs with treewidth at most 4 Discret. Math. (IF 0.8) Pub Date : 2024-03-08 Changhong Lu, Niping Yi
Gallai conjectured that every connected graph with vertices admits a decomposition into at most paths. The conjecture has been proved for some special cases. Recently, Botler et al. (2020) proved that Gallai's conjecture holds for graphs with treewidth at most 3. In this paper, we show that if is a graph with treewidth at most 4, then can be decomposed into at most paths or is isomorphic to , to ,
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Query complexity of Boolean functions on slices Discret. Math. (IF 0.8) Pub Date : 2024-03-06 F, a, r, z, a, n, , B, y, r, a, m, j, i
The slice of the Boolean cube is the set of all -bit strings with Hamming weight . We study the deterministic query complexity of Boolean functions on slices of the Boolean cube. We show that there exists a function on the balanced slice requiring queries. We observe that there is an explicit function on the balanced slice requiring queries based on independent sets in Johnson graphs. We also consider
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Extremal spectral radius and essential edge-connectivity Discret. Math. (IF 0.8) Pub Date : 2024-03-05 Yu Wang, Huiqiu Lin, Yingzhi Tian
An edge-cut of is essential if has at least two non-trivial components, the essential edge-connectivity of is the minimum cardinality over all essential edge-cuts of . In this paper, we determine the graphs attaining the maximum spectral radius among all graphs with minimum degree and essential edge-connectivity. Moreover, the extremal graphs are characterized. This generalizes some previous results
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An improved condition for a family of trees being determined by their generalized spectrum Discret. Math. (IF 0.8) Pub Date : 2024-03-04 Jie Yang, Wei Wang
A graph is said to be (DGS for short), if whenever is a graph such that and are cospectral with cospecral complements then is isomorphic to . Let be an -vertex graph with adjacency matrix and be the of , where is the all-one vector. A theorem of Wang shows that if is odd and square-free, then is DGS. The above condition is equivalent to that the Smith normal form of is , where is an odd and square-free
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On enumeration of pattern-avoiding Fishburn permutations Discret. Math. (IF 0.8) Pub Date : 2024-03-04 Yujie Du, Philip B. Zhang
In this paper, we prove two conjectures of Egge on enumeration of several classes of pattern-avoiding Fishburn permutations. Our results include enumerating Fishburn permutations avoiding the pattern 321 and one of the following three types of classical patterns: a pattern of size 4, two patterns of size 4, or a pattern of size 5.
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0-1 Tableaux and the p,q-Legendre-Stirling numbers of the second kind Discret. Math. (IF 0.8) Pub Date : 2024-03-04 Lora R. Du, Kathy Q. Ji
We define the -Legendre-Stirling numbers of the second kind, which reduce to the Legendre-Stirling numbers of the second kind discovered by Everitt, Littlejohn and Wellman when and and the -Legendre-Stirling numbers of the second kind introduced by Mongelli when . By introducing 0-1 tableaux of shape with even multiplicities, we give a combinatorial interpretation of the -Legendre-Stirling numbers
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The weak order on the hyperoctahedral group and the monomial basis for the Hopf algebra of signed permutations Discret. Math. (IF 0.8) Pub Date : 2024-03-04 H, o, u, y, i, , Y, u
We give a combinatorial description for the weak order on the hyperoctahedral group. This characterization is then used to analyze the order-theoretic properties of the shifted products of hyperoctahedral groups. It is shown that each shifted product is a disjoint union of some intervals, which can be convex embedded into a larger hyperoctahedral group. As an application, we investigate the monomial
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A constructive solution to the Oberwolfach problem with a large cycle Discret. Math. (IF 0.8) Pub Date : 2024-03-04 T, o, m, m, a, s, o, , T, r, a, e, t, t, a
For every 2-regular graph of order , the Oberwolfach problem asks whether there is a 2-factorization of ( odd) or minus a 1-factor ( even) into copies of . Posed by Ringel in 1967 and extensively studied ever since, this problem is still open.
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Proof of an explicit formula for a series from Ramanujan's Notebooks via tree functions Discret. Math. (IF 0.8) Pub Date : 2024-03-01 Ming-Jian Ding, Jiang Zeng
We prove a recent conjecture, due to Vigren and Dieckmann, about an explicit triple sum formula for a series from Ramanujan's Notebooks. We shall give two proofs: the first one is by evaluation and based on the identity [Display omitted] where is a Stirling number of the second kind, and the second one is combinatorial in nature and by induction.
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Frobenius-König theorem for classes of (0,±1)-matrices Discret. Math. (IF 0.8) Pub Date : 2024-03-01 Richard A. Brualdi, Geir Dahl
The Frobenius-König Theorem has a central role in combinatorial matrix theory; it characterizes when a -matrix contains a permutation matrix (meaning entrywise). Our goal is to investigate similar questions for -matrices, and a main result is a Frobenius-König Theorem for the class of -matrices with all row and column sums being 1. Moreover, some related results are shown for alternating sign matrices
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A generalization of Mneimneh's binomial sum of harmonic numbers Discret. Math. (IF 0.8) Pub Date : 2024-03-01 Takao Komatsu, Pin Wang
In a 2023 Discrete Mathematics article, Mneimneh introduced a remarkable formula for a binomial sum of harmonic numbers, defined by . This formula can be extended to the generalized harmonic numbers, where is replaced by for a positive integer . In this paper, we extend Mneimneh's formula to the generalized hyperharmonic numbers , and as a special case of this, to the generalized harmonic numbers when
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On Blecher and Knopfmacher's fixed points for integer partitions Discret. Math. (IF 0.8) Pub Date : 2024-02-27 Brian Hopkins, James A. Sellers
Recently, Blecher and Knopfmacher explored the notion of fixed points in integer partitions and hypothesized on the relative number of partitions with and without a fixed point. We resolve their open question by working fixed points into a growing number of interconnected partition statistics involving Frobenius symbols, Dyson's crank, and the mex (minimal excluded part). Also, we generalize the definition
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Explicit congruences for k-marked Durfee symbols Discret. Math. (IF 0.8) Pub Date : 2024-02-27 Olivia X.M. Yao
In 2007, Andrews introduced -marked Durfee symbols to give a combinatorial interpretation of 2th symmetrized moment of ranks of partitions of . Let denote the number of -marked Durfee symbols of . Bringmann, Garvan and Mahlburg proved that there exist infinitely many arithmetic progressions such that , where is a positive integer and is a prime. In addition, Keith proved that . Motivated by their works
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The A-spectral radius for path-factors in graphs Discret. Math. (IF 0.8) Pub Date : 2024-02-26 Sizhong Zhou, Yuli Zhang, Zhiren Sun
Let , and let be a connected graph of order with , where for , for , for and for . A spanning subgraph whose components are paths is said to be a path-factor. A -factor means a path-factor with each component being a path of order at least , where is an integer. The -spectral radius of is denoted by . In this paper, it is verified that has a -factor if , where is the largest root of . Furthermore,
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The complete value of the Turán number of 3K+1 Discret. Math. (IF 0.8) Pub Date : 2024-02-26 Liang Zhang, Jian-Hua Yin
The of a graph , denoted by , is the maximum number of edges of an -vertex simple graph having no as a subgraph. Let denote the disjoint union of copies of graph . There are very few cases when the Turán number is known exactly for . Erdős and Gallai determined for . Chen, Lu and Yuan determined for . In this paper, we further determine for .
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Strong stability of 3-wise t-intersecting families Discret. Math. (IF 0.8) Pub Date : 2024-02-22 Norihide Tokushige
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T-tetrominos in arithmetic progression Discret. Math. (IF 0.8) Pub Date : 2024-02-22 Emily Feller, Robert Hochberg
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Sufficient condition for (α,β) Somos 4 Hankel determinants Discret. Math. (IF 0.8) Pub Date : 2024-02-21 Ying Wang, Zihao Zhang
By using Sulanke-Xin continued fractions method, Xin proposed a recursion system to solve the Somos 4 Hankel determinant conjecture. We find Xin's recursion system indeed give a sufficient condition for Somos 4 sequences. This allows us to prove 4 conjectures of Barry on Somos 4 sequences in a unified way.
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D-index and Q-index for spanning trees with leaf degree at most k in graphs Discret. Math. (IF 0.8) Pub Date : 2024-02-20 Sizhong Zhou, Zhiren Sun, Hongxia Liu
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Graphs with isolation number equal to one third of the order Discret. Math. (IF 0.8) Pub Date : 2024-02-19 Magdalena Lemańska, Mercè Mora, María José Souto-Salorio
A set of vertices of a graph is isolating if the set of vertices not in and with no neighbor in is independent. The isolation number of , denoted by , is the minimum cardinality of an isolating set of . It is known that , if is a connected graph of order , , distinct from . The main result of this work is the characterisation of unicyclic and block graphs of order with isolating number equal to . Moreover
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Strongly even cycle decomposable non-planar line graphs Discret. Math. (IF 0.8) Pub Date : 2024-02-18 Wenzhong Liu, Dandan Wang, Liping Wang, Yan Yang
A graph is strongly even cycle decomposable if for every subdivision of with an even number of edges, the edges of can be partitioned into cycles of even length. Máčajová and Mazák asked whether the line graph of a simple 2-connected cubic graph is strongly even cycle decomposable. A result of Seymour implies that the line graph of every 2-connected planar cubic graph is strongly even cycle decomposable
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Subsequence frequency in binary words Discret. Math. (IF 0.8) Pub Date : 2024-02-18 Krishna Menon, Anurag Singh
The numbers we study in this paper are of the form , which is the number of binary words of length that contain the word (as a subsequence, not necessarily consecutive in the word) exactly times. Our motivation comes from the analogous study of pattern containment in permutations. In our first set of results, we obtain explicit expressions for for small values of . We then focus on words with at most
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Critical Problem for a q-analogue of polymatroids Discret. Math. (IF 0.8) Pub Date : 2024-02-18 Koji Imamura, Keisuke Shiromoto
The Critical Problem posed by H. Crapo and G.-C. Rota is one of the significant problems in matroid theory. It is the problem for finding the maximum dimension of a subspace that contains no member of a fixed subset of . The problem is also equivalent to finding the critical exponent of the associated matroid. In 1966, W.T. Tutte introduced the useful terminology of blocks which is one of the main
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On the maximum of the weighted binomial sum (1+a)−r∑i=0r(mi)ai Discret. Math. (IF 0.8) Pub Date : 2024-02-13 Seok Hyun Byun, Svetlana Poznanović
Recently, Glasby and Paseman considered the following sequence of binomial sums and showed that this sequence is unimodal and attains its maximum value at for . They also analyzed the asymptotic behavior of the maximum value of the sequence as approaches infinity. In the present work, we generalize their results by considering the sequence for integers . We also consider a family of discrete probability
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Distance-regular graphs with a few q-distance eigenvalues Discret. Math. (IF 0.8) Pub Date : 2024-02-12 Mamoon Abdullah, Brhane Gebremichel, Sakander Hayat, Jack H. Koolen
In this paper we study when the -distance matrix of a distance-regular graph has few distinct eigenvalues. We mainly concentrate on diameter 3.
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The classification of orthogonal arrays OA(2048,14,2,7) and some completely regular codes Discret. Math. (IF 0.8) Pub Date : 2024-02-09 Denis S. Krotov
We describe the classification of orthogonal arrays OA, or, equivalently, completely regular -codes in the 14-cube (30848 equivalence classes). In particular, we find that there is exactly one almost-OA, up to equivalence. As derived objects, OA (202917 classes) and completely regular - and -codes in the 13- and 14-cubes, respectively, are also classified.
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Forests and the strong Erdős-Hajnal property Discret. Math. (IF 0.8) Pub Date : 2024-02-09 Soukaina Zayat
Alon et al. proposed an equivalent directed version of the celebrated unresolved conjecture of Erdős and Hajnal which states that for every tournament there exists such that every -free -vertex tournament contains a transitive subtournament of order at least . A tournament H has the strong EH-property if there exists such that for every -free tournament with || >1, there exist disjoint vertex subsets
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BCH cyclic codes Discret. Math. (IF 0.8) Pub Date : 2024-02-09 Cunsheng Ding, Chengju Li
BCH codes are a subclass of cyclic codes with many interesting properties. In many cases BCH codes are the best linear codes. For example, among all binary cyclic codes of odd length with the best cyclic code is always a BCH code except for two special cases. Reed-Solomon codes are also BCH codes and are widely used in communication devices and consumer electronics. Binary BCH codes were discovered
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About S-packing coloring of subcubic graphs Discret. Math. (IF 0.8) Pub Date : 2024-02-09 Maidoun Mortada, Olivier Togni
For a non-decreasing sequence of integers , an -packing coloring of a graph is a partition of into subsets such that the distance between any two distinct vertices is at least , . This paper studies the packing coloring of subcubic graphs. Gastineau and Togni (2016) asked whether every subcubic graph except the Petersen graph is -packing colorable. A subcubic graph is said to be -saturated, , if every
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Constructions of strongly regular Cayley graphs derived from weakly regular bent functions Discret. Math. (IF 0.8) Pub Date : 2024-02-08 Liqin Qian, Xiwang Cao, Jerod Michel
In this paper, inspired by the work of Tan et al. (2010) , Chee et al. (2011) and Hyun et al. (2020) , we propose two new constructions of strongly regular graphs on finite fields by using weakly regular bent functions, which generalize the results in the existing references. We obtain two families of strongly regular graphs with flexible parameters. We are also able to obtain a 3-class amorphic association
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Connectivity keeping edges of trees in 3-connected or 3-edge-connected graphs Discret. Math. (IF 0.8) Pub Date : 2024-02-08 Qing Yang, Yingzhi Tian
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On a relationship between the characteristic and matching polynomials of a uniform hypertree Discret. Math. (IF 0.8) Pub Date : 2024-02-07 Honghai Li, Li Su, Shaun Fallat
A hypertree is a connected hypergraph without cycles. Further a hypertree is called an -tree if, additionally, it is -uniform. Note that 2-trees are just ordinary trees. A classical result states that for any 2-tree with characteristic polynomial and matching polynomial , then . More generally, suppose is an -tree of size with . In this paper, we extend the above classical relationship to -trees and
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New weighing matrices via partitioned group actions Discret. Math. (IF 0.8) Pub Date : 2024-02-06 Radel Ben-Av, Giora Dula, Assaf Goldberger, Ilias Kotsireas, Yossi Strassler
We solve the smallest four open cases of weighing matrices, for , which completes the existence question for weight 16. In addition we solve the open two-core matrix . There is a common theme for the construction of all such matrices, which is called here . The study of partitioned group matrices generalizes some well known constructions, namely the one-core and two-core circulant constructions, with
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Computing the fully optimal spanning tree of an ordered bipolar directed graph Discret. Math. (IF 0.8) Pub Date : 2024-02-06 Emeric Gioan, Michel Las Vergnas
It was previously shown by the authors that a directed graph on a linearly ordered set of edges (ordered graph) with adjacent unique source and sink (bipolar digraph) has a unique fully optimal spanning tree, that satisfies a simple criterion on fundamental cycle/cocycle directions. This result is related to a strengthening of the notion of optimality in linear programming. Furthermore, this result
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Splitting fields of some matrices of normal (mixed) Cayley graphs Discret. Math. (IF 0.8) Pub Date : 2024-02-06 Yongjiang Wu, Qinghong Guo, Jing Yang, Lihua Feng
The splitting field of a matrix associated with a graph is the smallest field extension of that contains all of its eigenvalues. The extension degree is called its algebraic degree. In this paper, by introducing a new characteristic vector for each normal subset of a finite group, we completely determine the splitting fields and algebraic degrees for the adjacency matrix and distance matrix of a normal
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On symmetric spectra of Hermitian adjacency matrices for non-bipartite mixed graphs Discret. Math. (IF 0.8) Pub Date : 2024-02-02 Yusuke Higuchi, Sho Kubota, Etsuo Segawa
We study the equivalence between bipartiteness and symmetry of spectra of mixed graphs, for -Hermitian adjacency matrices defined by an angle . We show that this equivalence holds when, for example, an angle is an algebraic number, while it breaks down for any angle . Furthermore, we construct a family of non-bipartite mixed graphs having the symmetric spectra for given .
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The clique graphs of the hexagonal lattice – an explicit construction and a short proof of divergence Discret. Math. (IF 0.8) Pub Date : 2024-02-02 Martin Winter
We present a new, explicit and very geometric construction for the iterated clique graphs of the hexagonal lattice Hex which makes apparent its clique divergence and sheds light on some previous observations, such as the boundedness of the degrees and clique sizes of as .
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Bipartite secret sharing and staircases Discret. Math. (IF 0.8) Pub Date : 2024-02-02 Laszlo Csirmaz, František Matúš, Carles Padró
Bipartite secret sharing schemes have a bipartite access structure in which the set of participants is divided into two parts and all participants in the same part play an equivalent role. Such a bipartite scheme can be described by a : the collection of its minimal points. The complexity of a scheme is the maximal share size relative to the secret size; and the -complexity of an access structure is
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Sparse critical graphs for defective DP-colorings Discret. Math. (IF 0.8) Pub Date : 2024-02-02 Alexandr Kostochka, Jingwei Xu
An interesting generalization of list coloring is so called DP-coloring (named after Dvořák and Postle). We study -defective DP-colorings of simple graphs. Define to be the minimum number of edges in an -vertex DP--critical graph. We prove sharp bounds on for and for infinitely many .
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Sum labelling graphs of maximum degree two Discret. Math. (IF 0.8) Pub Date : 2024-02-02 Henning Fernau, Kshitij Gajjar
The concept of was introduced in 1990 by Harary. A graph is a if its vertices can be labelled by distinct positive integers in such a way that two vertices are connected by an edge if and only if the sum of their labels is the label of another vertex in the graph. It is easy to see that every sum graph has at least one isolated vertex, and every graph can be made a sum graph by adding at most isolated
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The effects of semantic simplifications on random BST-like expression-trees Discret. Math. (IF 0.8) Pub Date : 2024-02-01 Florent Koechlin, Pablo Rotondo
In this article, we consider random expressions produced as BST-like trees (from the term BST, binary search trees), and study the effect of simple semantic reductions on them. These random trees are fast to produce and can be parametrized; that is why they are often used in benchmarks for model-checking tools. We assume the existence of an operator ⊛ that has an absorbing pattern and study the effect
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On the maximum number of maximum dissociation sets in trees with given dissociation number Discret. Math. (IF 0.8) Pub Date : 2024-02-01 Jianhua Tu, Lei Zhang, Junfeng Du
In a graph , a subset of vertices is a dissociation set if it induces a subgraph with vertex degree at most 1. A maximum dissociation set is a dissociation set of maximum cardinality. The dissociation number of , denoted by , is the cardinality of a maximum dissociation set of . Extremal problems involving counting the number of a given type of substructure in a graph have been a hot topic of study
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Resolutions of the designs in two infinite series of 4-designs Discret. Math. (IF 0.8) Pub Date : 2024-02-01 Tran van Trung
The resolutions of the designs in two infinite series of 4-designs constructed by Alltop and Hubaut are the subject of this study. We examine two types of resolutions, namely the -resolutions and the point-missing -resolutions. The result can essentially be stated that the designs possess 3-resolutions and point-missing -resolutions for subject to a necessary numerical condition of the parameters.
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A characterization of well-dominated Cartesian products Discret. Math. (IF 0.8) Pub Date : 2024-02-01 Kirsti Kuenzel, Douglas F. Rall
A graph is well-dominated if all its minimal dominating sets have the same cardinality. In this paper we prove that at least one factor of every connected, well-dominated Cartesian product is a complete graph, which then allows us to give a complete characterization of the connected, well-dominated Cartesian products if both factors have order at least 2. In particular, we show that is well-dominated
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Trivial colors in colorings of Kneser graphs Discret. Math. (IF 0.8) Pub Date : 2024-01-30 Sergei Kiselev, Andrey Kupavskii
We show that any proper coloring of a Kneser graph with colors contains a trivial color class (i.e., a color class consisting of sets that all contain a fixed element), provided , where as . This bound is essentially tight. This is a consequence of a more general result on the minimum number of non-trivial color classes needed to properly color .
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A characterization of optimal constacyclic locally repairable codes Discret. Math. (IF 0.8) Pub Date : 2024-01-26 Wei Zhao, Kenneth W. Shum, Shenghao Yang
A locally repairable code (LRC) with locality r allows for the recovery of any erased codeword symbol using at most r other codeword symbols. The Singleton-type bound dictates a best possible tradeoff between the dimension, the minimum distance and the locality of LRCs. An LRC attaining this tradeoff is said to be optimal. A constacyclic LRC is an LRC with constacyclic structure which can be encoded
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Orbit codes of finite Abelian groups and lattices Discret. Math. (IF 0.8) Pub Date : 2024-01-26 Sihem Mesnager, Rameez Raja
This paper constructs a class of lattices whose discrete analogues are variable-length non-linear codes. The well-known discrete analogue of lattices and linear codes inspires our approach. We next design a variable length binary non-linear code called automorphism orbit code from a finite abelian p-group of rank greater than 1, where p is a prime. For each finite abelian p-group, codewords of the
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The maximum designed distances of dual-containing non-primitive BCH codes Discret. Math. (IF 0.8) Pub Date : 2024-01-26 Fengwei Li, Qin Yue, Daitao Huang
Let q be a prime power and m a positive integer. Suppose that a≥2 is a factor of qm−1 such that m is the multiplicative order of q modulo n:=qm−1a. Firstly, for m odd and m even, we present some necessary and sufficient conditions on dual-containing non-primitive BCH codes of length n with the maximum designed distances over Fq, respectively. The results show that the maximum designed distances of
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Rotationally symmetric snarks from voltage graphs Discret. Math. (IF 0.8) Pub Date : 2024-01-25 Leah Wrenn Berman, Déborah Oliveros, Gordon I. Williams
In 1976, Loupekine introduced (via Isaacs) a very general way of constructing new snarks from old snarks by cyclically connecting multipoles constructed by pulling out a path of length 2 from smaller snarks. In this paper, we use Zm lifts of voltage graphs formed by a similar construction to produce a variety of snarks which can be drawn with m-fold rotational symmetry for m≥3. In particular, we discuss
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On a class of APN power functions over odd characteristic finite fields: Their differential spectrum and c-differential properties Discret. Math. (IF 0.8) Pub Date : 2024-01-23 Haode Yan, Sihem Mesnager, Xiantong Tan
The differential spectrum of a cryptographic function is of significant interest for estimating the resistance of the involved vectorial function to some variances of differential cryptanalysis. It is well-known that it is difficult to determine a power function's differential spectrum completely. In the present article, we concentrate on studying the differential and the c-differential uniformity
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On the restricted size Ramsey number for a pair of cycles Discret. Math. (IF 0.8) Pub Date : 2024-01-26 Tomasz Łuczak, Joanna Polcyn, Zahra Rahimi
For graphs by we denote the minimum number of edges in a graph on vertices such that . We show that for each pair of natural numbers , , where is odd and is large enough, we have