Multicolor Ramsey numbers for paths and cycles
Tomasz Dzido
Discussiones Mathematicae Graph Theory, Tome 25 (2005), p. 57-65 / Harvested from The Polish Digital Mathematics Library
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For given graphs G₁,G₂,...,Gₖ, k ≥ 2, the multicolor Ramsey number R(G₁,G₂,...,Gₖ) is the smallest integer n such that if we arbitrarily color the edges of the complete graph on n vertices with k colors, then it is always a monochromatic copy of some Gi, for 1 ≤ i ≤ k. We give a lower bound for k-color Ramsey number R(Cₘ,Cₘ,...,Cₘ), where m ≥ 8 is even and Cₘ is the cycle on m vertices. In addition, we provide exact values for Ramsey numbers R(P₃,Cₘ,Cₚ), where P₃ is the path on 3 vertices, and several values for R(Pₗ,Pₘ,Cₚ), where l,m,p ≥ 2. In this paper we present new results in this field as well as some interesting conjectures.

Publié le : 2005-01-01
EUDML-ID : urn:eudml:doc:270242 
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Tomasz Dzido. Multicolor Ramsey numbers for paths and cycles. Discussiones Mathematicae Graph Theory, Tome 25 (2005) pp. 57-65. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1260/

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