Complete solution for the rainbow numbers of matchings |
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Authors: | He Chen Jianhua Tu |
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Institution: | Center for Combinatorics and LPMC-TJKLC, Nankai University, Tianjin 300071, PR China |
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Abstract: | For a given graph H and a positive n, the rainbow number ofH, denoted by rb(n,H), is the minimum integer k so that in any edge-coloring of Kn with k colors there is a copy of H whose edges have distinct colors. In 2004, Schiermeyer determined rb(n,kK2) for all n≥3k+3. The case for smaller values of n (namely, ) remained generally open. In this paper we extend Schiermeyer’s result to all plausible n and hence determine the rainbow number of matchings. |
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Keywords: | Edge-colored graph Rainbow subgraph Rainbow number |
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