Výsledky vyhledávání - "Méroueh, Arès"

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List colourings of multipartite hypergraphs

Let $\chi_l(G)$ denote the list chromatic number of the $r$-uniform hypergraph~$G$. Extending a result of Alon for graphs, Saxton and the second author used the method of containers to prove that, if $G$ is simple and $d$-regular, then $\chi_l(G)\ge

Externí odkaz: http://arxiv.org/abs/1704.07907

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Lubell mass and induced partially ordered sets

Autor: Méroueh, Arès

We prove that for every partially ordered set $P$, there exists $c(P)$ such that every family $\mathcal{F}$ of subsets of $[n]$ ordered by inclusion and which contains no induced copy of $P$ satisfies $\sum_{F\in \mathcal{F}}1/{n\choose |F|}\leq c(P)

Externí odkaz: http://arxiv.org/abs/1506.07056

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The Ramsey number of loose cycles versus cliques

Autor: Méroueh, Arès

Recently Kostochka, Mubayi and Verstra\"ete initiated the study of the Ramsey numbers of uniform loose cycles versus cliques. In particular they proved that $R(C^r_3,K^r_n) = \tilde{\theta}(n^{3/2})$ for all fixed $r\geq 3$. For the case of loose cyc

Externí odkaz: http://arxiv.org/abs/1504.03668

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Catching a mouse on a tree

Autor: Gruslys, Vytautas, Méroueh, Arès

In this paper we consider a pursuit-evasion game on a graph. A team of cats, which may choose any vertex of the graph at any turn, tries to catch an invisible mouse, which is constrained to moving along the vertices of the graph. Our main focus shall

Externí odkaz: http://arxiv.org/abs/1502.06591

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On Forbidden Submatrices

Autor: Méroueh, Arès

Given a $k\times l$ $(0,1)$-matrix $F$, we denote by $\mathrm{fs}(m,F)$ the largest number for which there is an $m \times \mathrm{fs}(m,F)$ $(0,1)$-matrix with no repeated columns and no induced submatrix equal to $F$. A conjecture of Anstee, Frankl

Externí odkaz: http://arxiv.org/abs/1401.2102

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