Abstract
An edge colored graph is called a rainbow if no two of its edges have the same color. Let ℋ and \(\mathcal{G}\) be two families of graphs. Denote by \(RM({\mathcal{H}},\mathcal{G})\) the smallest integer R, if it exists, having the property that every coloring of the edges of K R by an arbitrary number of colors implies that either there is a monochromatic subgraph of K R that is isomorphic to a graph in ℋ or there is a rainbow subgraph of K R that is isomorphic to a graph in \(\mathcal{G}\) . \({\mathcal{T}}_{n}\) is the set of all trees on n vertices. \({\mathcal{T}}_{n}(k)\) denotes all trees on n vertices with diam(T n (k))≤k. In this paper, we investigate \(RM({\mathcal{T}}_{n},4K_{2})\) , \(RM({\mathcal{T}}_{n},K_{1,4})\) and \(RM({\mathcal{T}}_{n}(4),K_{3})\) .
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This research was supported by National Natural Science Foundation of China (10571042), NSF of Hebei (A2005000144) and the SF of Hebei Normal University (L2004202).
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Wei, X., Ding, R. More on monochromatic-rainbow Ramsey type theorems. J. Appl. Math. Comput. 27, 175–181 (2008). https://doi.org/10.1007/s12190-008-0059-y
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DOI: https://doi.org/10.1007/s12190-008-0059-y