科研之友
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摘要
We seek the maximum number of colors in an edgecoloring of the complete graph Kn not having t edge-disjoint rainbow spanning subgraphs of specified types. Let c(n, t), m(n, t), and r (n, t) denote the answers when the spanning subgraphs are cycles, matchings, or trees, respectively. We prove c(n, t) = ((n-1)(2)) + t for n >= 8t - 1 and m(n, t) = ((n-2)(2)) + t for n > 4t + 10. We prove r(n,t) = ((n-2)(2)) + t for n> 2t + root 6t - 23/4 + 5/2 and r(n, t) + ((n)(2)) - t for n = 2t We also provide constructions for the more general problem in which colorings are restricted so that colors do not appear on more than q edges at a vertex.
- 出版日期2016-5
- 单位浙江师范大学
