منابع مشابه
Planar Ramsey numbers for cycles
For two given graphs G and H the planar Ramsey number PR(G,H) is the smallest integer n such that every planar graph F on n vertices either contains a copy of G or its complement contains a copy H . By studying the existence of subhamiltonian cycles in complements of sparse graphs, we determine all planar Ramsey numbers for pairs of cycles.
متن کاملRamsey Numbers for Cycles in Graphs
Given two graphs G, , G2 , the Ramsey number R(G,, G2) is the smallest integer m such that, for any partition (E1 , E2) of the edges of K,,, , either G 1 is a subgraph of the graph induced by E1 , or G2 is a subgraph of the graph induced by E2. We show that R(C " , Cn) = 2n-1 if n is odd,
متن کاملRainbow Numbers for Cycles in Plane Triangulations
In the article, the existence of rainbow cycles in edge colored plane triangulations is studied. It is shown that the minimum number rb(Tn,C3) of colors that force the existence of a rainbow C3 in any n-vertex plane triangulation is equal to 3n−4 2 . For k ≥ 4 a lower bound and for k ∈ {4,5} an upper bound of the number rb(Tn,Ck ) is determined. C © 2014 Wiley Periodicals, Inc. J. Graph Theory ...
متن کاملMulticolor Ramsey Numbers for Paths and Cycles
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...
متن کاملRainbow Numbers for Graphs Containing Small Cycles
For a given graph H and n ≥ 1, let f(n,H) denote the maximum number m for which it is possible to colour the edges of the complete graph Kn with m colours in such a way that each subgraph H in Kn has at least two edges of the same colour. Equivalently, any edge-colouring of Kn with at least rb(n,H) = f(n,H) + 1 colours contains a rainbow copy of H. The numbers f(n,H) and rb(Kn, H) are called an...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2011
ISSN: 0012-365X
DOI: 10.1016/j.disc.2009.11.004