Results 101 to 110 of about 997,897 (240)
Journal of Combinatorial Designs, Volume 33, Issue 2, Page 58-71, February 2025.ABSTRACT We consider playing the game of Tic‐Tac‐Toe on block designs BIBD( v , k , λ ) $(v,k,\lambda )$ and transversal designs TD( k , n ) $(k,n)$. Players take turns choosing points and the first player to complete a block wins the game. We show that triple systems, BIBD( v , 3 , λ ) $(v,3,\lambda )$, are a first‐player win if and only if v ≥ 5 $v ...
Peter Danziger +3 more
wiley +1 more source
Improved bounds on the extremal function of hypergraphs [PDF]
arXiv, 2018 A fundamental problem in pattern avoidance is describing the asymptotic behavior of the extremal function and its generalizations. We prove an equivalence between the asymptotics of the graph extremal function for a class of bipartite graphs and the asymptotics of the matrix extremal function.
arxiv
Plains Zebras Prioritize Foraging Without Sacrificing Social Bonds During a Severe Drought
Ecology and Evolution, Volume 15, Issue 1, January 2025.We investigated how the highly social plains zebra (Equus quagga) modify their activity budgets, social networks, and multimodal communication during a drought. Although animals prioritized feeding and the number of social interactions dramatically decreased in the late drought period, social associations remained robust.
Severine B. S. W. Hex +2 more
wiley +1 more source
On the extremal Betti numbers of binomial edge ideals of block graphs [PDF]
arXiv, 2018 We compute one of the distinguished extremal Betti number of the binomial edge ideal of a block graph, and classify all block graphs admitting precisely one extremal Betti number.
arxiv
Freiman's theorem in finite fields via extremal set theory
, 2007 Using various results from extremal set theory (interpreted in the language of additive combinatorics), we prove an asyptotically sharp version of Freiman's theorem in F_2^n: if A in F_2^n is a set for which |A + A|
Green, Ben, Tao, Terence
core
Integer colorings with forbidden rainbow sums
, 2020 For a set of positive integers $A \subseteq [n]$, an $r$-coloring of $A$ is rainbow sum-free if it contains no rainbow Schur triple. In this paper we initiate the study of the rainbow Erd\H{o}s-Rothchild problem in the context of sum-free sets, which ...
Cheng, Yangyang +4 more
core
Dense H-free graphs are almost (Χ(H)-1)-partite [PDF]
, 2010 By using the Szemeredi Regularity Lemma, Alon and Sudakov recently extended the classical Andrasfai-Erdos-Sos theorem to cover general graphs. We prove, without using the Regularity Lemma, that the following stronger statement is true.
Allen, Peter
core +2 more sources
Upper Bounds for Linear Graph Codes
Random Structures &Algorithms, Volume 66, Issue 1, January 2025.ABSTRACT A linear graph code is a family 𝒞 of graphs on n$$ n $$ vertices with the property that the symmetric difference of the edge sets of any two graphs in 𝒞 is also the edge set of a graph in 𝒞. In this article, we investigate the maximal size of a linear graph code that does not contain a copy of a fixed graph H$$ H $$.
Leo Versteegen
wiley +1 more source
Immersions of Directed Graphs in Tournaments
Random Structures &Algorithms, Volume 66, Issue 1, January 2025.ABSTRACT Recently, Draganić, Munhá Correia, Sudakov and Yuster (2022) showed that every tournament on (2+o(1))k2$$ \left(2+o(1)\right){k}^2 $$ vertices contains a 1‐subdivision of a transitive tournament on k$$ k $$ vertices, which is tight up to a constant factor. We prove a counterpart of their result for immersions.
António Girão, Robert Hancock
wiley +1 more source
Intersection Problems in Extremal Combinatorics: Theorems, Techniques and Questions Old and New [PDF]
, 2022 Anthony Nixon +2 more
openalex +1 more source