Geodesic
Multicolor Ramsey numbers for paths and cycles
Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 1-2, pp. 57-65

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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 G_i, 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.
Keywords: edge coloring, Ramsey number 
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     title = {Multicolor {Ramsey} numbers for paths and cycles},
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Dzido, Tomasz. Multicolor Ramsey numbers for paths and cycles. Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 1-2, pp. 57-65. http://geodesic.mathdoc.fr/item/DMGT_2005_25_1-2_a6/