On Multicolor Ramsey Number of Paths Versus Cycles
نویسندگان
چکیده
منابع مشابه
On Multicolor Ramsey Number of Paths Versus Cycles
Let G1, G2, . . . , Gt be graphs. The multicolor Ramsey number R(G1, G2, . . . , Gt) is the smallest positive integer n such that if the edges of a complete graph Kn are partitioned into t disjoint color classes giving t graphs H1,H2, . . . ,Ht, then at least one Hi has a subgraph isomorphic to Gi. In this paper, we provide the exact value of R(Pn1 , Pn2 , . . . , Pnt , Ck) for certain values o...
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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...
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We show that if we color the hyperedges of the complete 3-uniform hypergraph on 2n + √ 18n + 1 + 2 vertices with n colors, then one of the color classes contains a loose path of length three. Let P denote the 3-uniform path of length three by which we mean the only connected 3-uniform hypergraph on seven vertices with the degree sequence (2, 2, 1, 1, 1, 1, 1). By R(P ;n) we denote the multicolo...
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Let F , G and H be simple graphs. We say F → (G,H) if for every 2-coloring of the edges of F there exists a monochromatic G orH in F . The Ramsey number r(G,H) is defined as r(G,H) = min{|V (F )| : F → (G,H)}, while the restricted size Ramsey number r(G,H) is defined as r(G,H) = min{|E(F )| : F → (G,H), |V (F )| = r(G,H)}. In this paper we determine previously unknown restricted size Ramsey num...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2011
ISSN: 1077-8926
DOI: 10.37236/511