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The tripartite Ramsey number for trees

✍ Scribed by Julia Böttcher; Jan Hladký; Diana Piguet

Book ID: 108120727
Publisher: Elsevier Science
Year: 2009
Tongue: English
Weight: 192 KB
Volume: 34
Category: Article
ISSN: 1571-0653
DOI: 10.1016/j.endm.2009.07.101

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📜 SIMILAR VOLUMES

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## Abstract We prove that for all ε>0 there are α>0 and __n__~0~∈ℕ such that for all __n__⩾__n__~0~ the following holds. For any two‐coloring of the edges of __K__~__n, n, n__~ one color contains copies of all trees __T__ of order __t__⩽(3 − ε)__n__/2 and with maximum degree Δ(__T__)⩽__n__^α^. This

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## Abstract In this article, we study the tripartite Ramsey numbers of paths. We show that in any two‐coloring of the edges of the complete tripartite graph __K__(__n__, __n__, __n__) there is a monochromatic path of length (1 − __o__(1))2__n__. Since __R__(__P__~2__n__+1~,__P__~2__n__+1~)=3__n__,

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In this note we find the local and mean k-Ramsey numbers for many trees for which the Erdo s So s tree conjecture holds. ## 2000 Academic Press The usual Ramsey number R(G, k) is the smallest positive integer n such that any coloring of the edges of K n by at most k colors contains a monochromatic

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It will be shown that the (diagonal) size Ramsey number of K ..... is bounded below by c. 64n , 2 3oj2 ~n 2 and above by 2 Let F and G be graphs. The symbol F >---,G denotes that in any two-colouring (say red and blue) of edges of F a monochromatic copy of G is contained. The Ramsey number r(G) is t