منابع مشابه
Trees with an On-Line Degree Ramsey Number of Four
On-line Ramsey theory studies a graph-building game between two players. The player called Builder builds edges one at a time, and the player called Painter paints each new edge red or blue after it is built. The graph constructed is called the background graph. Builder’s goal is to cause the background graph to contain a monochromatic copy of a given goal graph, and Painter’s goal is to preven...
متن کاملThe Ramsey Number for Hypergraph Cycles Ii
Let C (3) n denote the 3-uniform tight cycle, that is the hypergraph with vertices v1, . . . , vn and edges v1v2v3, v2v3v4, . . . , vn−1vnv1, vnv1v2. We prove that the smallest integer N = N(n) for which every red-blue coloring of the edges of the complete 3-uniform hypergraph with N vertices contains a monochromatic copy of C (3) n is asymptotically equal to 4n/3 if n is divisible by 3, and 2n...
متن کاملDegree Ramsey numbers for even cycles
Let H s − → G denote that any s-coloring of E(H) contains a monochromatic G. The degree Ramsey number of a graph G, denoted by R∆(G, s), is min{∆(H) : H s − → G}. We consider degree Ramsey numbers where G is a fixed even cycle. Kinnersley, Milans, and West showed that R∆(C2k, s) ≥ 2s, and Kang and Perarnau showed that R∆(C4, s) = Θ(s 2). Our main result is that R∆(C6, s) = Θ(s 3/2) and R∆(C10, ...
متن کاملOn 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...
متن کاملA multipartite Ramsey number for odd cycles
In this paper we study multipartite Ramsey numbers for odd cycles. Our main result is the proof of a conjecture of Gyárfás, Sárközy and Schelp [12]. Precisely, let n ≥ 5 be an arbitrary positive odd integer; then in any two-coloring of the edges of the complete 5-partite graph K(n−1)/2,(n−1)/2,(n−1)/2,(n−1)/2,1 there is a monochromatic cycle of length n. keywords: cycles, Ramsey number, Regular...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2013
ISSN: 0012-365X
DOI: 10.1016/j.disc.2013.04.020