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Binomial determinants for tiling problems yield to the holonomic ansatz Eur. J. Comb. (IF 0.847) Pub Date : 20210920
Hao Du, Christoph Koutschan, Thotsaporn Thanatipanonda, Elaine WongWe present and prove closed form expressions for some families of binomial determinants with signed Kronecker deltas that are located along an arbitrary diagonal in the corresponding matrix. They count cyclically symmetric rhombus tilings of hexagonal regions with triangular holes. We extend a previous systematic study of these families, where the locations of the Kronecker deltas depended on an additional

Linear Turán numbers of acyclic triple systems Eur. J. Comb. (IF 0.847) Pub Date : 20210915
András Gyárfás, Miklós Ruszinkó, Gábor N. SárközyThe Turán number of hypergraphs has been studied extensively. Here we deal with a recent direction, the linear Turán number, and restrict ourselves to linear triple systems, a collection of triples on a set of points in which any two triples intersect in at most one point. For a fixed linear triple system F, the linear Turán number exL(n,F) is the maximum number of triples in a linear triple system

Parametric restrictions on quasisymmetric designs Eur. J. Comb. (IF 0.847) Pub Date : 20210915
Bhaskar BagchiIn this paper, we attach several new invariants to connected strongly regular graphs (excepting conference graphs on nonsquare number of vertices): one invariant called the discriminant, and a padic invariant corresponding to each prime number p. We prove parametric restrictions on quasisymmetric 2designs with a given connected block graph G and a given defect (absolute difference of the two intersection

The mixing time of switch Markov chains: A unified approach Eur. J. Comb. (IF 0.847) Pub Date : 20210913
Péter L. Erdős, Catherine Greenhill, Tamás Róbert Mezei, István Miklós, Dániel Soltész, Lajos SoukupSince 1997 a considerable effort has been spent to study the mixing time of switch Markov chains on the realizations of graphic degree sequences of simple graphs. Several results were proved on rapidly mixing Markov chains on unconstrained, bipartite, and directed sequences, using different mechanisms. The aim of this paper is to unify these approaches. We will illustrate the strength of the unified

Block decomposition and statistics arising from permutation tableaux Eur. J. Comb. (IF 0.847) Pub Date : 20210903
Joanna N. ChenPermutation statistics wm¯ and rlm are both arising from permutation tableaux. wm¯ was introduced by Chen and Zhou, which was proved equally distributed with the number of unrestricted rows of a permutation tableau. While rlm is shown by Nadeau equally distributed with the number of 1’s in the first row of a permutation tableau. In this paper, we investigate the joint distribution of wm¯ and rlm. Statistic

Reconstructing a generalized quadrangle from the Penttila–Williford 4class association scheme Eur. J. Comb. (IF 0.847) Pub Date : 20210903
Giusy Monzillo, Alessandro SicilianoPenttila and Williford constructed a 4class association scheme from a generalized quadrangle with a doubly subtended subquadrangle. We show that an association scheme with appropriate parameters and satisfying some assumption about maximal cliques must be the Penttila–Williford scheme.

Quantitative Fractional Helly and (p,q)Theorems Eur. J. Comb. (IF 0.847) Pub Date : 20210903
Attila Jung, Márton NaszódiWe consider quantitative versions of Hellytype questions, that is, instead of finding a point in the intersection, we bound the volume of the intersection. Our first main result is a quantitative version of the Fractional Helly Theorem of Katchalski and Liu, the second one is a quantitative version of the (p,q)Theorem of Alon and Kleitman.

On the number of independent sets in uniform, regular, linear hypergraphs Eur. J. Comb. (IF 0.847) Pub Date : 20210901
Emma Cohen, Will Perkins, Michail Sarantis, Prasad TetaliWe study the problems of bounding the number weak and strong independent sets in runiform, dregular, nvertex linear hypergraphs with no crossedges. In the case of weak independent sets, we provide an upper bound that is tight up to the first order term for all (fixed) r≥3, with d and n going to infinity. In the case of strong independent sets, for r=3, we provide an upper bound that is tight up

Hamilton cycles in the semirandom graph process Eur. J. Comb. (IF 0.847) Pub Date : 20210902
Pu Gao, Bogumił Kamiński, Calum MacRury, Paweł PrałatThe semirandom graph process is a single player game in which the player is initially presented an empty graph on n vertices. In each round, a vertex u is presented to the player independently and uniformly at random. The player then adaptively selects a vertex v, and adds the edge uv to the graph. For a fixed monotone graph property, the objective of the player is to force the graph to satisfy this

Packing Apaths of length zero modulo four Eur. J. Comb. (IF 0.847) Pub Date : 20210901
Henning Bruhn, Arthur UlmerWe show that Apaths of length 0 modulo 4 have the Erdős–Pósa property. Modulus m=4 is the only composite number for which Apaths of length 0 modulo m have the property.

The spectral radius of graphs with no odd wheels Eur. J. Comb. (IF 0.847) Pub Date : 20210827
Sebastian Cioabă, Dheer Noal Desai, Michael TaitThe odd wheel W2k+1 is the graph formed by joining a vertex to a cycle of length 2k. In this paper, we investigate the largest value of the spectral radius of the adjacency matrix of an nvertex graph that does not contain W2k+1. We determine the structure of the spectral extremal graphs for all k≥2,k⁄∈{4,5}. When k=2, we show that these spectral extremal graphs are among the Turánextremal graphs

Distinguishing index of graphs with simple automorphism groups Eur. J. Comb. (IF 0.847) Pub Date : 20210820
Mariusz Grech, Andrzej KisielewiczThe distinguishing index D′(Γ) of a graph Γ is the least number k such that Γ has an edgecoloring with k colors preserved only by the trivial automorphism. In this paper we prove that if the automorphism group of a finite graph Γ is simple, then its distinguishing index D′(Γ)=2.

A quadratic identity in the shuffle algebra and an alternative proof for de Bruijn’s formula Eur. J. Comb. (IF 0.847) Pub Date : 20210819
Laura Colmenarejo, Joscha Diehl, MirunaŞtefana SoreaMotivated by a polynomial identity of certain iterated integrals, first observed in Colmenarejo et al. (2020) in the setting of lattice paths, we prove an intriguing combinatorial identity in the shuffle algebra. It has a close connection to de Bruijn’s formula when interpreted in the framework of signatures of paths.

Finite type invariants for knotoids Eur. J. Comb. (IF 0.847) Pub Date : 20210814
Manousos Manouras, Sofia Lambropoulou, Louis H. KauffmanWe extend the theory of Vassiliev (or finite type) invariants for knots to knotoids using two different approaches. Firstly, we take closures on knotoids to obtain knots and we use the Vassiliev invariants for knots, proving that these are knotoid isotopy invariant. Secondly, we define finite type invariants directly on knotoids, by extending knotoid invariants to singular knotoid invariants via the

Quasirandom words and limits of word sequences Eur. J. Comb. (IF 0.847) Pub Date : 20210810
Hiệp Hàn, Marcos Kiwi, Matías PavezSignéWords are sequences of letters over a finite alphabet. We study two intimately related topics for this object: quasirandomness and limit theory. With respect to the first topic we investigate the notion of uniform distribution of letters over intervals, and in the spirit of the famous Chung–Graham–Wilson theorem for graphs we provide a list of word properties which are equivalent to uniformity. In

Schröder combinatorics and νassociahedra Eur. J. Comb. (IF 0.847) Pub Date : 20210809
Matias von Bell, Martha YipWe study νSchröder paths, which are Schröder paths which stay weakly above a given lattice path ν. Some classical bijective and enumerative results are extended to the νsetting, including the relationship between small and large Schröder paths. We introduce two posets of νSchröder objects, namely νSchröder paths and trees, and show that they are isomorphic to the face poset of the νassociahedron

Bounds on expected propagation time of probabilistic zero forcing Eur. J. Comb. (IF 0.847) Pub Date : 20210807
Shyam Narayanan, Alec SunProbabilistic zero forcing is a coloring game played on a graph where the goal is to color every vertex blue starting with an initial blue vertex set. As long as the graph G is connected, if at least 1 vertex is blue then eventually all of the vertices will be colored blue. The most studied parameter in probabilistic zero forcing is the expected propagation time ept(G). We significantly improve on

On the cover Turán number of Berge hypergraphs Eur. J. Comb. (IF 0.847) Pub Date : 20210805
Linyuan Lu, Zhiyu WangFor a fixed set of positive integers R, we say H is an Runiform hypergraph, or Rgraph, if the cardinality of each edge belongs to R. For a graph G=(V,E), a hypergraph H is called a BergeG, if there is an injection i:V(G)→V(H) and a bijection f:E(G)→E(H) such that for all e=uv∈E(G), we have {i(u),i(v)}⊆f(e). We define the cover Turán number of a graph G, denoted as exˆR(n,BG), as the maximum number

On the Baer–Lovász–Tutte construction of groups from graphs: Isomorphism types and homomorphism notions Eur. J. Comb. (IF 0.847) Pub Date : 20210729
Xiaoyu He, Youming QiaoLet p be an odd prime. From a simple undirected graph G, through the classical procedures of Baer (1938), Tutte (1947) and Lovász (1989), there is a pgroup PG of class 2 and exponent p that is naturally associated with G. Our first result is to show that this construction of groups from graphs respects isomorphism types. That is, given two graphs G and H, G and H are isomorphic as graphs if and only

Corrigendum to “Some doubly transitive bilinear dual hyperovals and their ambient spaces” [European J. Combin. 44 (2015) 1–22] Eur. J. Comb. (IF 0.847) Pub Date : 20210727
Ulrich DempwolffWe correct an error in proof of the author’s Theorem [1, Thm. 4.1].

An improved linear connectivity bound for tournaments to be highly linked Eur. J. Comb. (IF 0.847) Pub Date : 20210720
Wei Meng, Martin Rolek, Yue Wang, Gexin YuA digraph is klinked if for any two disjoint sets of vertices {x1,…,xk} and {y1,…,yk} there are vertex disjoint paths P1,…,Pk such that Pi is directed from xi to yi for i=1,…,k. Pokrovskiy in 2015 proved that every strongly 452kconnected tournament is klinked. In this paper, we significantly reduce this connectivity bound and show that any (40k−31)connected tournament is klinked.

Zero sum cycles in complete digraphs Eur. J. Comb. (IF 0.847) Pub Date : 20210720
Tamás Mészáros, Raphael SteinerGiven a nontrivial finite Abelian group (A,+), let n(A)≥2 be the smallest integer such that for every labelling of the arcs of the bidirected complete graph K↔n(A) with elements from A there exists a directed cycle for which the sum of the arclabels is zero. The problem of determining n(Zq) for integers q≥2 was recently considered by Alon and Krivelevich, (2020), who proved that n(Zq)=O(qlogq). Here

On incidences of lines in regular complexes Eur. J. Comb. (IF 0.847) Pub Date : 20210720
Misha RudnevA regular linear line complex is a threeparameter set of lines in space, whose Plücker vectors lie in a hyperplane, which is not tangent to the Klein quadric. Our main result is a bound O(n1∕2m3∕4+m+n) for the number of incidences between n lines in a complex and m points in F3, where F is a field, and n≤char(F)4∕3 in positive characteristic. Zahl has recently observed that bichromatic pairwise incidences

Some coefficient sequences related to the descent polynomial Eur. J. Comb. (IF 0.847) Pub Date : 20210717
Ferenc BencsThe descent polynomial of a finite I⊆Z+ is the polynomial d(I,n), for which the evaluation at n>max(I) is the number of permutations on n elements, such that I is the set of indices where the permutation is descending. In this paper, we will prove some conjectures concerning coefficient sequences of d(I,n). As a corollary, we will describe some zerofree regions for the descent polynomial.

On regular set systems containing regular subsystems Eur. J. Comb. (IF 0.847) Pub Date : 20210713
Amin Bahmanian, Sadegheh HaghshenasLet X,Y be finite sets, r,s,h,λ∈N with s≥r,X⊊Y. By λXh we mean the collection of all hsubsets of X where each subset occurs λ times. A coloring (partition) of λXh is rregular if each element of X is in exactly r subsets of each color. A oneregular color class is a perfect matching. We are interested in necessary and sufficient conditions under which an rregular coloring of λXh can be embedded into

On the treewidth of evenholefree graphs Eur. J. Comb. (IF 0.847) Pub Date : 20210712
Pierre Aboulker, Isolde Adler, Eun Jung Kim, Ni Luh Dewi Sintiari, Nicolas TrotignonThe class of all evenholefree graphs has unbounded treewidth, as it contains all complete graphs. Recently, a class of (evenhole, K4)free graphs was constructed, that still has unbounded treewidth (Sintiari and Trotignon, 2019). The class has unbounded degree and contains arbitrarily large cliqueminors. We ask whether this is necessary. We prove that for every graph G, if G excludes a fixed

Primitive elements of the Hopf algebras of tableaux Eur. J. Comb. (IF 0.847) Pub Date : 20210708
C. Malvenuto, C. ReutenauerThe character theory of symmetric groups, and the theory of symmetric functions, both make use of the combinatorics of Young tableaux, such as the Robinson–Schensted algorithm, Schützenberger’s “jeu de taquin”, and evacuation. In 1995 Poirier and the second author introduced some algebraic structures, different from the plactic monoid, which induce some products and coproducts of tableaux, with homomorphisms

On qanalogs of descent and peak polynomials Eur. J. Comb. (IF 0.847) Pub Date : 20210707
Christian Gaetz, Yibo GaoDescent polynomials and peak polynomials, which enumerate permutations π∈Sn with given descent and peak sets respectively, have recently received considerable attention (Billey et al., 1989;DiazLopez et al., 2019). We give several formulas for qanalogs of these polynomials which refine the enumeration by the length of π. In the case of qdescent polynomials we prove that the coefficients in one basis

On the maximum mean subtree order of trees Eur. J. Comb. (IF 0.847) Pub Date : 20210706
Stijn Cambie, Stephan Wagner, Hua WangA subtree of a tree is any induced subgraph that is again a tree (i.e., connected). The mean subtree order of a tree is the average number of vertices of its subtrees. This invariant was first analyzed in the 1980s by Jamison. An intriguing open question raised by Jamison asks whether the maximum of the mean subtree order, given the order of the tree, is always attained by some caterpillar. While we

4connected polyhedra have at least a linear number of hamiltonian cycles Eur. J. Comb. (IF 0.847) Pub Date : 20210706
Gunnar Brinkmann, Nico Van CleemputAlthough polyhedra can have much fewer edges than triangulations, many results about hamiltonicity proven for triangulations also hold for polyhedra. The most famous of these results is surely Whitney’s result from 1931 that 4connected triangulations are hamiltonian, which was 25 years later generalised to 4connected polyhedra by Tutte. Nevertheless the only known bounds for the number of hamiltonian

On bipartite graphs with exactly one irreducible Tmodule with endpoint 1, which is thin Eur. J. Comb. (IF 0.847) Pub Date : 20210703
Blas Fernández, Štefko MiklavičLet Γ denote a finite, simple, connected and bipartite graph. Fix a vertex x of Γ and let T=T(x) denote the Terwilliger algebra of Γ with respect to x. Assume that x is a distanceregularized vertex, which is not a leaf. We consider the property that Γ has, up to isomorphism, a unique irreducible Tmodule with endpoint 1, and that this Tmodule is thin. The main result of the paper is a combinatorial

Tight bounds for Katona’s shadow intersection theorem Eur. J. Comb. (IF 0.847) Pub Date : 20210702
Xizhi Liu, Dhruv MubayiA fundamental result in extremal set theory is Katona’s shadow intersection theorem, which extends the Kruskal–Katona theorem by giving a lower bound on the size of the shadow of an intersecting family of ksets in terms of its size. We improve this classical result and a related result of Ahlswede, Aydinian and Khachatrian by proving tight bounds for families that can be quite small. For example,

Locally restricted compositions over a finite group Eur. J. Comb. (IF 0.847) Pub Date : 20210628
Zhicheng Gao, Andrew MacFieOne may generalize integer compositions by replacing the positive integers with a different additive semigroup, giving the broader concept of a “composition over a semigroup”. Here we focus on semigroups which are finite groups and achieve asymptotic enumeration of compositions over a finite group which satisfy a local restriction. These compositions are associated to walks on a voltage graph whose

On graphs whose second largest eigenvalue is at most 1 Eur. J. Comb. (IF 0.847) Pub Date : 20210625
Muhuo Liu, Chaohui Chen, Zoran StanićWe determine all connected {K1,3,K5−e}free graphs whose second largest eigenvalue does not exceed 1. Our result includes all connected line graphs with the same spectral property, and therefore strengthens the result of Petrović and Milekić (1998).

The structure of large nontrivial tintersecting families of finite sets Eur. J. Comb. (IF 0.847) Pub Date : 20210621
Mengyu Cao, Benjian Lv, Kaishun WangIn this paper, we describe the structure of maximal nontrivial uniform tintersecting families with large size for finite sets. In the special case when t=1, our result gives rise to Kostochka and Mubayi’s result in 2017.

Cops and robbers on directed and undirected abelian Cayley graphs Eur. J. Comb. (IF 0.847) Pub Date : 20210616
Peter Bradshaw, Seyyed Aliasghar Hosseini, Jérémie TurcotteWe show that the cop number of directed and undirected Cayley graphs on abelian groups is in O(n), where n is the number of vertices, by introducing a refined inductive method. With our method, we improve the previous upper bound on cop number for undirected Cayley graphs on abelian groups, and we establish an upper bound on the cop number of directed Cayley graphs on abelian groups. We also use Cayley

Chen and Chvátal’s conjecture in tournaments Eur. J. Comb. (IF 0.847) Pub Date : 20210614
Gabriela AraujoPardo, Martín MatamalaIn a directed graph D, given two distinct vertices u and v, the line defined by the ordered pair (u,v) is the set of all vertices w such that u,v and w belong to a shortest directed path in D, containing a shortest directed path from u to v. In this work we study the following conjecture: the number of distinct lines in any strongly connected graph is at least its number of vertices, unless there is

Bijective link between Chapoton’s new intervals and bipartite planar maps Eur. J. Comb. (IF 0.847) Pub Date : 20210614
Wenjie FangIn 2006, Chapoton defined a class of Tamari intervals called ”new intervals” in his enumeration of Tamari intervals, and he found that these new intervals are equienumerated with bipartite planar maps. We present here a direct bijection between these two classes of objects using a new object called ”degree tree”. Our bijection also gives an intuitive proof of an unpublished equidistribution result

qdimensions of highest weight crystals and cyclic sieving phenomenon Eur. J. Comb. (IF 0.847) Pub Date : 20210612
YoungTak Oh, Euiyong ParkIn this paper, we compute explicitly the qdimensions of highest weight crystals modulo qn−1 for a quantum group of arbitrary finite type under certain assumption, and interpret the modulo computations in terms of the cyclic sieving phenomenon. This interpretation gives an affirmative answer to the conjecture by Alexandersson and Amini. As an application, under the assumption that λ is a partition

Jacobian elliptic functions and a family of bivariate peak polynomials Eur. J. Comb. (IF 0.847) Pub Date : 20210612
ShiMei Ma, Jun Ma, YeongNan Yeh, Roberta R. ZhouThe Jacobian elliptic function sn(u,k) is the inverse of the elliptic integral of the first kind and cn(u,k)=1−sn2(u,k). In this paper, we study coefficient polynomials in the Taylor series expansions of sn(u,k) and cn(u,k). We first provide a combinatorial expansion for a family of bivariate peak polynomials, which count permutations by their odd and even cycle peaks. A special case of this combinatorial

Maximizing fivecycles in Krfree graphs Eur. J. Comb. (IF 0.847) Pub Date : 20210610
Bernard Lidický, Kyle MurphyThe Pentagon Problem of Erdős problem asks to find an nvertex trianglefree graph that is maximizing the number of 5cycles. The problem was solved using flag algebras by Grzesik and independently by Hatami, Hladký, Král’, Norin, and Razborov. Recently, Palmer suggested a more general problem of maximizing the number of 5cycles in Kk+1free graphs. Using flag algebras, we show that every Kk+1free

On λfold relative Heffter arrays and biembedding multigraphs on surfaces Eur. J. Comb. (IF 0.847) Pub Date : 20210607
Simone Costa, Anita PasottiIn this paper we define a new class of partially filled arrays, called λfold relative Heffter arrays, that are a generalization of the Heffter arrays introduced by Archdeacon in 2015. After showing the connection of this new concept with several other ones, such as signed magic arrays, graph decompositions and relative difference families, we determine some necessary conditions and we present existence

On a conjecture of Gross, Mansour and Tucker Eur. J. Comb. (IF 0.847) Pub Date : 20210603
Sergei Chmutov, Fabien VignesTourneretPartial duality is a duality of ribbon graphs relative to a subset of their edges generalizing the classical Euler–Poincaré duality. This operation often changes the genus. Recently J.L. Gross, T. Mansour, and T.W. Tucker formulated a conjecture that for any ribbon graph different from plane trees and their partial duals, there is a subset of edges partial duality relative to which does change the

On the chromatic number of the preferential attachment graph Eur. J. Comb. (IF 0.847) Pub Date : 20210529
Lyuben LichevWe prove that for every m∈N and every δ∈(−m,0), the chromatic number of the preferential attachment graph PAt(m,δ) is asymptotically almost surely equal to m+1. The proof relies on a combinatorial construction of a family of digraphs of chromatic number m+1 followed by a proof that asymptotically almost surely there is a digraph in this family, which is realised as a subgraph of the preferential attachment

Orientablyregular maps of Euler characteristic −2p2 Eur. J. Comb. (IF 0.847) Pub Date : 20210528
Jicheng MaConder and the author (Conder and Ma, 2015) studied the orientablyregular maps with simple underlying graphs and showed that there exists at least one orientablyregular map of genus g⁄≡2mod6 with simple underlying graph, and Conder conjectured that there exists at least one for every positive integer g. In this paper, we give a classification of all orientablyregular maps of Euler characteristic

Zonotopes whose cellular strings are all coherent Eur. J. Comb. (IF 0.847) Pub Date : 20210521
Rob Edman, Pakawut Jiradilok, Gaku Liu, Thomas McConvilleA cellular string of a polytope is a sequence of faces stacked on top of each other in a given direction. The poset of cellular strings, ordered by refinement, is known to be homotopy equivalent to a sphere. The subposet of coherent cellular strings is the face lattice of the fiber polytope, hence is homeomorphic to a sphere. In some special cases, every cellular string is coherent. Such polytopes

Connected hypergraphs without long Bergepaths Eur. J. Comb. (IF 0.847) Pub Date : 20210507
Ervin Győri, Nika Salia, Oscar ZamoraWe generalize a result of Balister, Győri, Lehel and Schelp for hypergraphs. We determine the unique extremal structure of an nvertex runiform connected hypergraph with the maximum number of hyperedges, without a kBergepath, where n≥Nk,r, k≥2r+13>17.

Ball packings for links Eur. J. Comb. (IF 0.847) Pub Date : 20210508
Jorge L. Ramírez Alfonsín, Iván RasskinThe ball number of a link L, denoted by ball(L), is the minimum number of solid balls (not necessarily of the same size) needed to realize a necklace representing L. In this paper, we show that ball(L)≤5cr(L) where cr(L) denotes the crossing number of a nontrivial nonsplittable link L. To this end, we use the connection of the Lorentz geometry with the ball packings. The wellknown Koebe–Andreev–Thurston

Twoarctransitive graphs of odd order — II Eur. J. Comb. (IF 0.847) Pub Date : 20210508
Cai Heng Li, Jing Jian Li, Zai Ping LuIt is shown that each subgroup of odd index in an alternating group of degree at least 10 has all insoluble composition factors to be alternating. A classification is then given of 2arctransitive graphs of odd order admitting an alternating group or a symmetric group. This is the second of a series of papers aiming towards a classification of 2arctransitive graphs of odd order.

Injective edgecoloring of graphs with given maximum degree Eur. J. Comb. (IF 0.847) Pub Date : 20210507
Alexandr Kostochka, André Raspaud, Jingwei XuA coloring of edges of a graph G is injective if for any two distinct edges e1 and e2, the colors of e1 and e2 are distinct if they are at distance 1 in G or in a common triangle. Naturally, the injective chromatic index of G, χinj′(G), is the minimum number of colors needed for an injective edgecoloring of G. We study how large can be the injective chromatic index of G in terms of maximum degree

Waiter–Client trianglefactor game on the edges of the complete graph Eur. J. Comb. (IF 0.847) Pub Date : 20210507
Vojtěch DvořákConsider the following game played by two players, called Waiter and Client, on the edges of Kn (where n is divisible by 3). Initially, all the edges are unclaimed. In each round, Waiter picks two yet unclaimed edges. Client then chooses one of these two edges to be added to Waiter’s graph and one to be added to Client’s graph. Waiter wins if she forces Client to create a K3factor in Client’s graph

Choosing between incompatible ideals Eur. J. Comb. (IF 0.847) Pub Date : 20210507
Will Brian, Paul B. LarsonSuppose I and J are proper ideals on some set X. We say that I and J are incompatible if I∪J does not generate a proper ideal. Equivalently, I and J are incompatible if there is some A⊆X such that A∈I and X∖A∈J. If some B⊆X is either in I∖J or in J∖I, then we say that B chooses between I and J. We consider the following Ramseytheoretic problem: Given several pairs (I1,J1),(I2,J2),…,(Ik,Jk) of incompatible

New short proofs to some stability theorems Eur. J. Comb. (IF 0.847) Pub Date : 20210503
Xizhi LiuWe present new short proofs to both the exact and the stability result of two extremal problems. The first result is about the extension of Turán’s theorem to hypergraphs, and the second result is about cancellative hypergraphs. Our proofs are concise and straightforward, but give a sharper version of stability theorems to both problems.

Generalized spectral characterizations of almost controllable graphs Eur. J. Comb. (IF 0.847) Pub Date : 20210429
Wei Wang, Fenjin Liu, Wei WangCharacterizing graphs by their spectra is an important topic in spectral graph theory, which has attracted a lot of attention of researchers in recent years. It is generally very hard and challenging to show a given graph is determined by its spectrum. In Wang (2017), the author gave a simple arithmetic condition for a family of graphs being determined by their generalized spectra. However, the method

A bound for 1cross intersecting set pair systems Eur. J. Comb. (IF 0.847) Pub Date : 20210427
Ron HolzmanA wellknown result of Bollobás says that if {(Ai,Bi)}i=1m is a set pair system such that Ai≤a and Bi≤b for 1≤i≤m, and Ai∩Bj≠0̸ if and only if i≠j, then m≤a+ba. Füredi, Gyárfás and Király recently initiated the study of such systems with the additional property that Ai∩Bj=1 for all i≠j. Confirming a conjecture of theirs, we show that this extra condition allows an improvement of the upper bound

Coloring graphs by translates in the circle Eur. J. Comb. (IF 0.847) Pub Date : 20210427
Pablo Candela, Carlos Catalá, Robert Hancock, Adam Kabela, Daniel Král’, Ander Lamaison, Lluís VenaThe fractional and circular chromatic numbers are the two most studied nonintegral refinements of the chromatic number of a graph. Starting from the definition of a coloring base of a graph, which originated in work related to ergodic theory, we formalize the notion of a gyrocoloring of a graph: the vertices are colored by translates of a single Borel set in the circle group, and neighboring vertices

Improved bounds on the Ramsey number of fans Eur. J. Comb. (IF 0.847) Pub Date : 20210426
Guantao Chen, Xiaowei Yu, Yi ZhaoFor a given graph H, the Ramsey number r(H) is the minimum N such that any 2edgecoloring of the complete graph KN yields a monochromatic copy of H. Given a positive integer n, a fanFn is a graph formed by n triangles that share one common vertex. We show that 9n∕2−5≤r(Fn)≤11n∕2+6 for any n. This improves previous best bounds r(Fn)≤6n of Lin and Li and r(Fn)≥4n+2 of Zhang, Broersma and Chen.

Berge–Fulkerson coloring for some families of superposition snarks Eur. J. Comb. (IF 0.847) Pub Date : 20210423
Siyan Liu, RongXia Hao, CunQuan ZhangIt is conjectured by Berge and Fulkerson that every bridgeless cubic graph has six perfect matchings such that each edge is contained in exactly two of them. This conjecture has been verified for many families of snarks with small (≤5) cyclic edgeconnectivity. An infinite family, denoted by SK, of cyclically 6edgeconnected superposition snarks was constructed in [European J. Combin. 2002] by Kochol

Partial duality for ribbon graphs, II: Partialtwuality polynomials and monodromy computations Eur. J. Comb. (IF 0.847) Pub Date : 20210421
Jonathan L. Gross, Toufik Mansour, Thomas W. TuckerThe partial (Poincaré) dual with respect to a subset A of edges of a ribbon graph G was introduced by Chmutov in connection with the Jones–Kauffman and Bollobás–Riordan polynomials. In developing the theory of maps, Wilson and others have composed Poincaré duality ∗ with Petrie duality × to give Wilson duality ∗×∗ and two trialities ∗× and ×∗. In further expanding the theory, Abrams and EllisMonaghan

Old and new applications of Katona’s circle Eur. J. Comb. (IF 0.847) Pub Date : 20210418
Peter FranklThe present paper is to honour Gyula Katona, my teacher on the occasion of his 80th birthday. Its main content is threefold, new proofs of old results (e.g. the De Bonis, Katona, Swanepoel Theorem on butterflyfree families), new results obtained via the Katona Circle (e.g. for the sum of the sizes of nonempty crossintersecting families), the solution for the Katona Circle of some notoriously difficult