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Pré-publication, Document de travail Année : 2014

Ramsey for complete graphs with dropped cliques

Résumé

Let $K_{[k,t]}$ be the complete graph on $k$ vertices from which a set of edges, induced by a clique of order $t$, has been dropped. In this note we give two explicit upper bounds for $R(K_{[k_1,t_1]},\dots, K_{[k_r,t_r]})$ (the smallest integer $n$ such that for any $r$-edge coloring of $K_n$ there always occurs a monochromatic $K_{[k_i,t_i]}$ for some $i$). Our first upper bound contains a classical one in the case when $k_1=\cdots =k_r$ and $t_i=1$ for all $i$. The second one is obtained by introducing a new edge coloring called $\chi_r$-colorings. We finally discuss a conjecture claiming, in particular, that our second upper bound improves the classical one in infinitely many cases.
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Dates et versions

hal-00847564, version 1 (23-07-2013)
hal-00847564, version 2 (24-07-2014)
hal-00847564, version 3 (12-12-2014)

Identifiants

  • HAL Id : hal-00847564 , version 3
  • ARXIV : 1307.6327

Citer

Jonathan Chappelon, Luis Pedro Montejano, Jorge Luis Ramírez Alfonsín. Ramsey for complete graphs with dropped cliques. 2014. ⟨hal-00847564v3⟩
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