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Some non-existence results on m-ovoids in classical polar spaces Eur. J. Comb. (IF 1.0) Pub Date : 2024-03-01 Jan De Beule, Jonathan Mannaert, Valentino Smaldore
In this paper we develop non-existence results for -ovoids in the classical polar spaces and for . In Bamberg et al. (2009) a lower bound on for the existence of -ovoids of is found by using the connection between -ovoids, two-character sets, and strongly regular graphs. This approach is generalized in Bamberg et al. (2007) for the polar spaces and , . In Bamberg et al. (2012) an improvement for the
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Initial nonrepetitive complexity of regular episturmian words and their Diophantine exponents Eur. J. Comb. (IF 1.0) Pub Date : 2024-02-29 Jarkko Peltomäki
Regular episturmian words are episturmian words whose directive words have a regular and restricted form making them behave more like Sturmian words than general episturmian words. We present a method to evaluate the initial nonrepetitive complexity of regular episturmian words extending the work of Wojcik on Sturmian words. For this, we develop a theory of generalized Ostrowski numeration systems
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Minimum degree conditions for containing an r-regular r-connected spanning subgraph Eur. J. Comb. (IF 1.0) Pub Date : 2024-02-26 Max Hahn-Klimroth, Olaf Parczyk, Yury Person
We study optimal minimum degree conditions when an -vertex graph contains an -regular -connected spanning subgraph. We prove for fixed and large the condition to be when . This answers a question of M. Kriesell.
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Overpartitions and Bressoud’s conjecture, II Eur. J. Comb. (IF 1.0) Pub Date : 2024-02-22 Thomas Y. He, Kathy Q. Ji, Alice X.H. Zhao
The main objective of this paper is to present an answer to Bressoud’s conjecture for the case , resulting in a complete solution to Bressoud’s conjecture. The case for has been recently resolved by Kim. Using the connection established in our previous paper between the ordinary partition function and the overpartition function , we found that the proof of Bressoud’s conjecture for the case is equivalent
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Homomorphisms between graphs embedded in surfaces Eur. J. Comb. (IF 1.0) Pub Date : 2024-02-22 Delia Garijo, Andrew Goodall, Lluís Vena
We extend the notion of graph homomorphism to cellularly embedded graphs (maps) by designing operations on vertices and edges that respect the surface topology; we thus obtain the first definition of map homomorphism that preserves both the combinatorial structure (as a graph homomorphism) and the topological structure of the surface (in particular, orientability and genus). Notions such as the core
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Characteristic sets of matroids Eur. J. Comb. (IF 1.0) Pub Date : 2024-02-22 Dustin Cartwright, Dony Varghese
We investigate possible linear, algebraic, and Frobenius flock characteristic sets of matroids. In particular, we classify possible combinations of linear and algebraic characteristic sets when the algebraic characteristic set is finite or cofinite. We also show that the natural density of an algebraic characteristic set in the set of primes may be arbitrarily close to any real number in the unit interval
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Homomorphisms to small negative even cycles Eur. J. Comb. (IF 1.0) Pub Date : 2024-02-22 Jiaao Li, Yongtang Shi, Zhouningxin Wang, Chunyan Wei
A strengthening of Jaeger’s circular flow conjecture, restricted to planar graphs, asserts that every planar graph of odd girth at least admits a homomorphism to the odd cycle , and the first case is verified and known as the famous Grötzsch theorem. In this paper, we prove analogous results for signed planar graphs: For every signed bipartite planar graph of negative girth at least admits a homomorphism
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On k-neighborly reorientations of oriented matroids Eur. J. Comb. (IF 1.0) Pub Date : 2024-02-17 Rangel Hernández-Ortiz, Kolja Knauer, Luis Pedro Montejano
We study the existence and the number of -neighborly reorientations of an oriented matroid. This leads to -variants of McMullen’s problem and Roudneff’s conjecture, the case being the original statements. Adding to results of Larman and García-Colín, we provide new bounds on -McMullen’s problem and prove the conjecture for several ranks and by computer. Further, we show that -Roudneff’s conjecture
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Hamilton completion and the path cover number of sparse random graphs Eur. J. Comb. (IF 1.0) Pub Date : 2024-02-15 Yahav Alon, Michael Krivelevich
We prove that for every there is such that if , , then with high probability can be covered by at most vertex disjoint paths, which is essentially tight. This is equivalent to showing that, with high probability, at most edges can be added to to create a Hamiltonian graph.
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Extremal numbers of hypergraph suspensions of even cycles Eur. J. Comb. (IF 1.0) Pub Date : 2024-02-15 Sayan Mukherjee
For fixed , determining the order of magnitude of the number of edges in an -vertex bipartite graph not containing , the cycle of length , is a long-standing open problem. We consider an extension of this problem to triple systems. In particular, we prove that the maximum number of triples in an -vertex triple system which does not contain a in the link of any vertex, has order of magnitude . Additionally
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Deletion–contraction and the surface Tutte polynomial Eur. J. Comb. (IF 1.0) Pub Date : 2024-02-13 Iain Moffatt, Maya Thompson
In this paper we unify two families of topological Tutte polynomials. The first family is that coming from the surface Tutte polynomial, a polynomial that arises in the theory of local flows and tensions. The second family arises from the canonical Tutte polynomials of Hopf algebras. Each family includes the Las Vergnas, Bollobás–Riordan, and Krushkal polynomials. As a consequence we determine a deletion–contraction
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Braid graphs in simply-laced triangle-free Coxeter systems are partial cubes Eur. J. Comb. (IF 1.0) Pub Date : 2024-02-08 Fadi Awik, Jadyn Breland, Quentin Cadman, Dana C. Ernst
In this paper, we study the structure of braid graphs in simply-laced Coxeter systems. We prove that every reduced expression has a unique factorization as a product of so-called links, which in turn induces a decomposition of the braid graph into a box product of the braid graphs for each link factor. When the Coxeter graph has no three-cycles, we use the decomposition to prove that braid graphs are
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Characterizations of families of morphisms and words via binomial complexities Eur. J. Comb. (IF 1.0) Pub Date : 2024-02-03 Michel Rigo, Manon Stipulanti, Markus A. Whiteland
Two words are -binomially equivalent if each subword of length at most occurs the same number of times in both words. The -binomial complexity of an infinite word is a counting function that maps to the number of -binomial equivalence classes represented by its factors of length . Cassaigne et al. (2011) characterized a family of morphisms, which we call Parikh-collinear, as those morphisms that map
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Stability of extremal connected hypergraphs avoiding Berge-paths Eur. J. Comb. (IF 1.0) Pub Date : 2024-02-02 Dániel Gerbner, Dániel T. Nagy, Balázs Patkós, Nika Salia, Máté Vizer
A Berge-path of length in a hypergraph is a sequence of distinct vertices and hyperedges with , for . Füredi, Kostochka and Luo, and independently Győri, Salia and Zamora determined the maximum number of hyperedges in an -vertex, connected, -uniform hypergraph that does not contain a Berge-path of length provided is large enough compared to . They also determined the unique extremal hypergraph .
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Max-norm Ramsey theory Eur. J. Comb. (IF 1.0) Pub Date : 2024-02-01 Nóra Frankl, Andrey Kupavskii, Arsenii Sagdeev
Given a metric space that contains at least two points, the chromatic number is defined as the minimum number of colours needed to colour all points of an -dimensional space with the max-norm such that no isometric copy of is monochromatic. The last two authors have recently shown that the value grows exponentially for all finite . In the present paper we refine this result by giving the exact value
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Delta-matroids whose twist polynomials are monomials Eur. J. Comb. (IF 1.0) Pub Date : 2024-02-01 Daniel Yuschak
The twist polynomial of a delta-matroid was recently introduced by Yan and Jin, who proved a characterization of binary delta-matroids whose twist polynomials are monomials. In this paper, we extend this result to all delta-matroids by proving that any delta-matroid whose twist polynomial is a monomial must be binary.
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Improved incidence bounds over arbitrary finite fields via the VC-dimension theory Eur. J. Comb. (IF 1.0) Pub Date : 2024-01-26 Alex Iosevich, Thang Pham, Steven Senger, Michael Tait
In this paper, we use tools from the theory of VC-dimension to study incidence problems over arbitrary finite fields. More precisely, we obtain improvements of Vinh’s result (2011) in three dimensions and a result on the intersection of planes.
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On the number of tangencies among 1-intersecting x-monotone curves Eur. J. Comb. (IF 1.0) Pub Date : 2024-01-25 Eyal Ackerman, Balázs Keszegh
Let C be a set of curves in the plane such that no three curves in C intersect at a single point and every pair of curves in C intersect at exactly one point which is either a crossing or a touching point. János Pach conjectured that the number of pairs of curves in C that touch each other is O(|C|). We prove this conjecture for x-monotone curves.
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The excluded minors for the intersection of bicircular and lattice path matroids Eur. J. Comb. (IF 1.0) Pub Date : 2024-01-27 Emma Hogan, Charles Semple
The classes of bicircular matroids and lattice path matroids are closed under minors. The complete list of excluded minors for the class of lattice path matroids is known, and it has been recently shown that the analogous list for the class of bicircular matroids is finite. In this paper, we establish the complete list of excluded minors for the class of matroids that is the intersection of these two
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Exact values and improved bounds on k-neighborly families of boxes Eur. J. Comb. (IF 1.0) Pub Date : 2024-01-20 Xinbu Cheng, Meiqin Wang, Zixiang Xu, Chi Hoi Yip
A finite family F of d-dimensional convex polytopes is called k-neighborly if d−k⩽dim(C∩C′)⩽d−1 for any two distinct members C,C′∈F. In 1997, Alon initiated the study of the general function n(k,d), which is defined to be the maximum size of k-neighborly families of standard boxes in Rd. Based on a weighted count of vectors in {0,1}d, we improve a recent upper bound on n(k,d) by Alon, Grytczuk, Kisielewicz
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Ann wins the nonrepetitive game over four letters and the erase-repetition game over six letters Eur. J. Comb. (IF 1.0) Pub Date : 2024-01-20 Matthieu Rosenfeld
We consider two games between two players Ann and Ben who build a word together by adding alternatively a letter at the end of a shared word. In the nonrepetitive game, Ben wins the game if he can create a square of length at least 4, and Ann wins if she can build an arbitrarily long word without Ben winning. In the erase-repetition game, whenever a square occurs the second part of the square is erased
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Minimum weight Euclidean (1+ɛ)-spanners Eur. J. Comb. (IF 1.0) Pub Date : 2024-01-22 Csaba D. Tóth
Given a set S of n points in the plane and a parameter ɛ>0, a Euclidean (1+ɛ)-spanner is a geometric graph G=(S,E) that contains, for all p,q∈S, a pq-path of weight at most (1+ɛ)‖pq‖. We show that the minimum weight of a Euclidean (1+ɛ)-spanner for n points in the unit square [0,1]2 is O(ɛ−3/2n), and this bound is the best possible. The upper bound is based on a new spanner algorithm in the plane.
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Online coloring of short intervals Eur. J. Comb. (IF 1.0) Pub Date : 2024-01-16 Joanna Chybowska-Sokół, Grzegorz Gutowski, Konstanty Junosza-Szaniawski, Patryk Mikos, Adam Polak
We study the online graph coloring problem restricted to the intersection graphs of intervals with lengths in [1,σ]. For σ=1 it is the class of unit interval graphs and for σ=∞ the class of all interval graphs. Our focus is on intermediary classes. We present a (1+σ)-competitive algorithm, which beats the state of the art for 1<σ<2, and proves that the problem we study can be strictly easier than online
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Vertex-weighted digraphs and freeness of arrangements between Shi and Ish Eur. J. Comb. (IF 1.0) Pub Date : 2024-01-15 Takuro Abe, Tan Nhat Tran, Shuhei Tsujie
We introduce and study a digraph analogue of Stanley’s ψ-graphical arrangements from the perspectives of combinatorics and freeness. Our arrangements form a common generalization of various classes of arrangements in the literature including the Catalan arrangement, the Shi arrangement, the Ish arrangement, and especially the arrangements interpolating between Shi and Ish, recently introduced by Duarte
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Ramsey numbers of cliques versus monotone paths Eur. J. Comb. (IF 1.0) Pub Date : 2024-01-12 Dhruv Mubayi, Andrew Suk
One formulation of the Erdős-Szekeres monotone subsequence theorem states that for any red/blue coloring of the edge set of the complete graph on , there exists a monochromatic red -clique or a monochromatic blue increasing path with vertices, provided . Here, we prove a similar statement as above in the off-diagonal case for triple systems, with the quasipolynomial bound . For the th power of the
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Bipartite Ramsey numbers of cycles Eur. J. Comb. (IF 1.0) Pub Date : 2024-01-12 Zilong Yan, Yuejian Peng
Let , …, be bipartite graphs. The bipartite Ramsey number is the minimum integer such that any -edge-coloring of the complete bipartite graph contains a monochromatic in color for some . The study of bipartite Ramsey number was initiated in the early 70s by Faudree and Schelp (1975), and they showed that , where denotes a path with vertices. Combining their result and the regularity lemma, one can
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Improved upper bound on the Frank number of 3-edge-connected graphs Eur. J. Comb. (IF 1.0) Pub Date : 2024-01-03 János Barát, Zoltán L. Blázsik
In an orientation O of the graph G, an arc e is deletable if and only if O−e is strongly connected. For a 3-edge-connected graph G, the Frank number is the minimum k for which G admits k strongly connected orientations such that for every edge e of G the corresponding arc is deletable in at least one of the k orientations. Hörsch and Szigeti conjectured the Frank number is at most 3 for every 3-edge-connected
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Clique covers of H-free graphs Eur. J. Comb. (IF 1.0) Pub Date : 2023-12-28 Tung Nguyen, Alex Scott, Paul Seymour, Stéphan Thomassé
It takes n2/4 cliques to cover all the edges of a complete bipartite graph Kn/2,n/2, but how many cliques does it take to cover all the edges of a graph G if G has no Kt,t induced subgraph? We prove that O(n2−1/(2t)) cliques suffice for every n-vertex graph; and also prove that, even for graphs with no stable set of size four, we may need more than linearly many cliques. This settles two questions
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Improved bounds for the dimension of divisibility Eur. J. Comb. (IF 1.0) Pub Date : 2023-12-28 Victor Souza, Leo Versteegen
The dimension of a partially-ordered set P is the smallest integer d such that one can embed P into a product of d linear orders. We prove that the dimension of the divisibility order on the interval {1,…,n} is bounded above by C(logn)2(loglogn)−2logloglogn as n goes to infinity. This improves a recent result by Lewis and the first author, who showed an upper bound of C(logn)2(loglogn)−1 and a lower
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Preface Eur. J. Comb. (IF 1.0) Pub Date : 2023-12-21 Daniel Král, Michał Pilipczuk, Sebastian Siebertz, Blair Sullivan
Abstract not available
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Excedance-type polynomials, gamma-positivity and alternatingly increasing property Eur. J. Comb. (IF 1.0) Pub Date : 2023-12-21 Shi-Mei Ma, Jun Ma, Jean Yeh, Yeong-Nan Yeh
In this paper, we first give a sufficient condition for a sequence of polynomials to have alternatingly increasing property, and then we present a systematic study of excedance-type polynomials of permutations and derangements, signed or not, colored or not. Let p∈[0,1] and q∈[0,1] be two given real numbers. We prove that the cyc q-Eulerian polynomials of permutations are bi-γ-positive, and the fix
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Saturation numbers for Berge cliques Eur. J. Comb. (IF 1.0) Pub Date : 2023-12-18 Sean English, Jürgen Kritschgau, Mina Nahvi, Elizabeth Sprangel
Let F be a graph and H be a hypergraph, both embedded on the same vertex set. We say H is a Berge-F if there exists a bijection ϕ:E(F)→E(H) such that e⊆ϕ(e) for all e∈E(F). We say H is Berge-F-saturated if H does not contain any Berge-F, but adding any missing edge to H creates a copy of a Berge-F. The saturation number satk(n,Berge-F) is the least number of edges in a Berge-F-saturated k-uniform hypergraph
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Reconfiguration of vertex colouring and forbidden induced subgraphs Eur. J. Comb. (IF 1.0) Pub Date : 2023-12-18 Manoj Belavadi, Kathie Cameron, Owen Merkel
The reconfiguration graph of the k-colourings, denoted Rk(G), is the graph whose vertices are the k-colourings of G and two colourings are adjacent in Rk(G) if they differ in colour on exactly one vertex. In this paper, we investigate the connectivity and diameter of Rk+1(G) for a k-colourable graph G restricted by forbidden induced subgraphs. We show that Rk+1(G) is connected for every k-colourable
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On the intersection density of the Kneser graph K(n,3) Eur. J. Comb. (IF 1.0) Pub Date : 2023-12-11 Karen Meagher, Andriaherimanana Sarobidy Razafimahatratra
A set F⊂Sym(V) is intersecting if any two of its elements agree on some element of V. Given a finite transitive permutation group G≤Sym(V), the intersection density ρ(G) is the maximum ratio |F||V||G| where F runs through all intersecting sets of G. The intersection density ρ(X) of a vertex-transitive graph X=(V,E) is equal to maxρ(G):G≤Aut(X),G transitive. In this paper, we study the intersection
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Additive structure in convex translates Eur. J. Comb. (IF 1.0) Pub Date : 2023-12-11 Gabriel Currier, Jozsef Solymosi, Ethan Patrick White
Let P be a set of points in the plane, and S a strictly convex set of points. In this note, we show that if P contains many translates of S, then these translates must come from a generalized arithmetic progression of low dimension. We also discuss an application to the unit distance conjecture.
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The Ehrhart and face polynomials of the graph polytope of a cycle Eur. J. Comb. (IF 1.0) Pub Date : 2023-12-06 Richard Ehrenborg
We are interested in the polytope consisting of all points in the first orthant such that the sum of two cyclically adjacent coordinates is less than or equal to 1. This polytope is also known as the graph polytope of a cycle. Using spectral techniques, we obtain a determinant for the Ehrhart quasi-polynomial of this polytope and hence also an expression for the volume of this polytope. The spectral
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q-Stirling numbers in type B Eur. J. Comb. (IF 1.0) Pub Date : 2023-12-06 Bruce E. Sagan, Joshua P. Swanson
Stirling numbers of the first and second kind, which respectively count permutations in the symmetric group and partitions of a set, have found extensive application in combinatorics, geometry, and algebra. We study analogues and q-analogues of these numbers corresponding to the Coxeter group of type B. In particular, we show how they are related to complete homogeneous and elementary symmetric polynomials;
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A nonlinear bound for the number of subsequence sums Eur. J. Comb. (IF 1.0) Pub Date : 2023-12-04 Vsevolod F. Lev
We show that a finite, zero-sum-free sequence α over an abelian group determines at least c|α|4/3 distinct subsequence sums, unless the sequence is “well-controlled” by a small number of its terms; here |α| denotes the number of terms of α, and c>0 is an absolute constant.
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Strictly increasing and decreasing sequences in subintervals of words and a conjecture of Guo and Poznanović Eur. J. Comb. (IF 1.0) Pub Date : 2023-12-05 Jonathan S. Bloom, Dan Saracino
We prove a conjecture of Guo and Poznanović concerning chains in certain 01-fillings of moon polyominoes. A key ingredient of our proof is a correspondence between words w and pairs (W(w),M(w)) of increasing tableaux such that M(w) determines the lengths of the longest strictly increasing and strictly decreasing sequences in every subinterval of w. We define this correspondence by using Thomas and
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Kempe changes in degenerate graphs Eur. J. Comb. (IF 1.0) Pub Date : 2023-11-21 Marthe Bonamy, Vincent Delecroix, Clément Legrand–Duchesne
We consider Kempe changes on the k-colorings of a graph on n vertices. If the graph is (k−1)-degenerate, then all its k-colorings are equivalent up to Kempe changes. However, the sequence between two k-colorings that arises from the proof may have length exponential in the number of vertices. An intriguing open question is whether it can be turned polynomial. We prove this to be possible under the
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Improved bounds on the maximum diversity of intersecting families Eur. J. Comb. (IF 1.0) Pub Date : 2023-11-17 Peter Frankl, Jian Wang
A family F⊂[n]k is called an intersecting family if F∩F′≠0̸ for all F,F′∈F. If ∩F≠0̸ then F is called a star. The diversity of an intersecting family F is defined as the minimum number of k-sets in F, whose deletion results in a star. In the present paper, we prove that for n>36k any intersecting family F⊂[n]k has diversity at most n−3k−2, which improves the previous best bound n>72k due to the first
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Structure of a sequence with prescribed zero-sum subsequences: Rank two p-groups Eur. J. Comb. (IF 1.0) Pub Date : 2023-11-20 John J. Ebert, David J. Grynkiewicz
Let G=(Z/nZ)⊕(Z/nZ). Let s≤k(G) be the smallest integer ℓ such that every sequence of ℓ terms from G, with repetition allowed, has a nonempty zero-sum subsequence with length at most k. It is known that s≤2n−1−k(G)=2n−1+k for k∈[0,n−1]. The structure of extremal sequences that show this bound is tight was determined for k∈{0,1,n−1}, and for various special cases when k∈[2,n−2]. For the remaining values
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Minimising the total number of subsets and supersets Eur. J. Comb. (IF 1.0) Pub Date : 2023-11-20 Adam Gowty, Daniel Horsley, Adam Mammoliti
Let F be a family of subsets of a ground set {1,…,n} with |F|=m, and let F↕ denote the family of all subsets of {1,…,n} that are subsets or supersets of sets in F. Here we determine the minimum value that |F↕| can attain as a function of n and m. This can be thought of as a ‘two-sided’ Kruskal–Katona style result. It also gives a solution to the isoperimetric problem on the graph whose vertices are
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Ramsey–Turán problems with small independence numbers Eur. J. Comb. (IF 1.0) Pub Date : 2023-11-21 József Balogh, Ce Chen, Grace McCourt, Cassie Murley
Given a graph H and a function f(n), the Ramsey–Turán number RT(n,H,f(n)) is the maximum number of edges in an n-vertex H-free graph with independence number at most f(n). For H being a small clique, many results about RT(n,H,f(n)) are known and we focus our attention on H=Ks for s≤13. By applying Szemerédi’s Regularity Lemma, the dependent random choice method and some weighted Turán-type results
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The spectral radius of minor-free graphs Eur. J. Comb. (IF 1.0) Pub Date : 2023-11-17 Ming-Zhu Chen, A-Ming Liu, Xiao-Dong Zhang
In this paper, we present a sharp upper bound for the spectral radius of an n-vertex F-minor-free graph for sufficiently large n, where F is obtained from the complete graph Kr by deleting disjoint paths. Furthermore, the graphs which achieve the sharp bound are characterized. This result may be regarded as a spectral extremal analogue of the number of edges in an n-vertex F-minor-free graph.
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An algebraic approach for counting DP-3-colorings of sparse graphs Eur. J. Comb. (IF 1.0) Pub Date : 2023-11-17 Samantha L. Dahlberg, Hemanshu Kaul, Jeffrey A. Mudrock
DP-coloring (or correspondence coloring) is a generalization of list coloring that has been widely studied since its introduction by Dvořák and Postle in 2015. As the analogue of the chromatic polynomial of a graph G, P(G,m), and the list color function, Pℓ(G,m), the DP-color function of G, denoted by PDP(G,m), counts the minimum number of DP-colorings over all possible m-fold covers. It follows that
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Off-diagonal online size Ramsey numbers for paths Eur. J. Comb. (IF 1.0) Pub Date : 2023-11-18 Małgorzata Bednarska-Bzdȩga
Consider the following Ramsey game played on the edge set of KN. In every round, Builder selects an edge and Painter colours it red or blue. Builder’s goal is to force Painter to create a red copy of a path Pk on k vertices or a blue copy of Pn as soon as possible. The online (size) Ramsey number r̃(Pk,Pn) is the number of rounds in the game provided Builder and Painter play optimally. We prove that
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Some memories Eur. J. Comb. (IF 1.0) Pub Date : 2023-11-18 Marc Bousset, Michel Imbert, Armelle Vanot, Philippe Gallic
Abstract not available
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Prime vertex-minors of a prime graph Eur. J. Comb. (IF 1.0) Pub Date : 2023-11-17 Donggyu Kim, Sang-il Oum
A graph is prime if it does not admit a partition (A,B) of its vertex set such that min{|A|,|B|}≥2 and the rank of the A×B submatrix of its adjacency matrix is at most 1. A vertex v of a graph is non-essential if at least two of the three kinds of vertex-minor reductions at v result in prime graphs. In 1994, Allys proved that every prime graph with at least four vertices has a non-essential vertex
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The rotation distance of brooms Eur. J. Comb. (IF 1.0) Pub Date : 2023-11-17 Jean Cardinal, Lionel Pournin, Mario Valencia-Pabon
The associahedron A(G) of a graph G has the property that its vertices can be thought of as the search trees on G and its edges as the rotations between two search trees. If G is a simple path, then A(G) is the usual associahedron and the search trees on G are binary search trees. Computing distances in the graph of A(G), or equivalently, the rotation distance between two binary search trees, is a
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On an extremal problem for locally sparse multigraphs Eur. J. Comb. (IF 1.0) Pub Date : 2023-11-17 Victor Falgas-Ravry
A multigraph G is an (s,q)-graph if every s-set of vertices in G supports at most q edges of G, counting multiplicities. Mubayi and Terry posed the problem of determining the maximum of the product of the edge-multiplicities in an (s,q)-graph on n vertices. We give an asymptotic solution to this problem for the family (s,q)=(2r,a2r2+ex(2r,Kr+1)−1) with r,a∈Z≥2. This greatly generalises previous results
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Graph-codes Eur. J. Comb. (IF 1.0) Pub Date : 2023-11-14 Noga Alon
The symmetric difference of two graphs G1,G2 on the same set of vertices [n]={1,2,…,n} is the graph on [n] whose set of edges are all edges that belong to exactly one of the two graphs G1,G2. Let H be a fixed graph with an even (positive) number of edges, and let DH(n) denote the maximum possible cardinality of a family of graphs on [n] containing no two members whose symmetric difference is a copy
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Rainbow clique subdivisions Eur. J. Comb. (IF 1.0) Pub Date : 2023-11-14 Yan Wang
We show that for any integer t≥2, every properly edge colored n-vertex graph with average degree at least (logn)2+o(1) contains a rainbow subdivision of a complete graph of size t. Note this bound is within (logn)1+o(1) factor of the lower bound. This also implies a result on the rainbow Turán number of cycles.
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On Helly numbers of exponential lattices Eur. J. Comb. (IF 1.0) Pub Date : 2023-11-14 Gergely Ambrus, Martin Balko, Nóra Frankl, Attila Jung, Márton Naszódi
Given a set S⊆R2, define the Helly number of S, denoted by H(S), as the smallest positive integer N, if it exists, for which the following statement is true: for any finite family F of convex sets in R2 such that the intersection of any N or fewer members of F contains at least one point of S, there is a point of S common to all members of F. We prove that the Helly numbers of exponential lattices
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Decomposing a triangle-free planar graph into a forest and a subcubic forest Eur. J. Comb. (IF 1.0) Pub Date : 2023-11-14 Carl Feghali, Robert Šámal
We strengthen a result of Dross et al. (2017) that the vertex set of every triangle-free planar graph can be decomposed into a set that induces a forest and a set that induces a forest with maximum degree at most 5, showing that 5 can be replaced by 3.
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Shuffle squares and reverse shuffle squares Eur. J. Comb. (IF 1.0) Pub Date : 2023-11-14 Xiaoyu He, Emily Huang, Ihyun Nam, Rishubh Thaper
Let SSk(n) be the family of shuffle squares in [k]2n, words that can be partitioned into two disjoint identical subsequences. Let RSSk(n) be the family of reverse shuffle squares in [k]2n, words that can be partitioned into two disjoint subsequences which are reverses of each other. Henshall, Rampersad, and Shallit conjectured asymptotic formulas for the sizes of SSk(n) and RSSk(n) based on numerical
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Composition closed premodel structures and the Kreweras lattice Eur. J. Comb. (IF 1.0) Pub Date : 2023-11-15 Scott Balchin, Ethan MacBrough, Kyle Ormsby
We investigate the rich combinatorial structure of premodel structures on finite lattices whose weak equivalences are closed under composition. We prove that there is a natural refinement of the inclusion order of weak factorization systems so that the intervals detect these composition closed premodel structures. In the case that the lattice in question is a finite total order, this natural order
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On the enumeration of plane bipolar posets and transversal structures Eur. J. Comb. (IF 1.0) Pub Date : 2023-11-16 Éric Fusy, Erkan Narmanli, Gilles Schaeffer
We show that plane bipolar posets (i.e., plane bipolar orientations with no transitive edge) and transversal structures can be set in correspondence to certain (weighted) models of quadrant walks, via suitable specializations of a bijection due to Kenyon, Miller, Sheffield and Wilson. We then derive exact and asymptotic counting results. In particular we prove (computationally and then bijectively)
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Preface | European Journal of Combinatorics Eur. J. Comb. (IF 1.0) Pub Date : 2023-10-31 Jaroslav Nešetřil, Guillem Perarnau, Juanjo Rué, Oriol Serra
Abstract not available