Multicolor Ramsey numbers for paths and cycles

• Autorzy: Tomasz Dzido
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

edge coloring; Ramsey number

Kategorie tematyczne

• 05C15: Coloring of graphs and hypergraphs
• 05C55: Generalized Ramsey theory

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2005
• Tom: 25
• Numer: 1-2
• Strony: 57-65

Daty

wydano

2005

otrzymano

2003-10-30

poprawiono

2005-01-28

Twórcy

autor

Tomasz Dzido

• Department of Computer Science, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland

Bibliografia

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Identyfikatory

DOI

10.7151/dmgt.1260