Anti-Ramsey Number of Edge-Disjoint Rainbow Spanning Trees
نویسندگان
چکیده
منابع مشابه
Anti-Ramsey Problems for t Edge-Disjoint Rainbow Spanning Subgraphs: Cycles, Matchings, or Trees
We seek the maximum number of colors in an edge-coloring 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) = ( 2 ) + t for n ≥ 8t − 1 and m(n, t) = ( 2 ) + t for n > 4t + 10. We prove r(n, t) = ( 2 ) + t...
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Let G be an edge-colored copy of Kn, where each color appears on at most n/2 edges (the edgecoloring is not necessarily proper). A rainbow spanning tree is a spanning tree of G where each edge has a different color. Brualdi and Hollingsworth [4] conjectured that every properly edge-colored Kn (n ≥ 6 and even) using exactly n−1 colors has n/2 edge-disjoint rainbow spanning trees, and they proved...
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where the minimum is taken over all subsets X of E(G) such that ω(G − X) − c > 0. In this paper, we establish a relationship 7 between λc(G) and τc−1(G), which gives a characterization of the edge-connectivity of a graph G in terms of the spanning tree 8 packing number of subgraphs of G. The digraph analogue is also obtained. The main results are applied to show that if a graph G is 9 s-hamilto...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2020
ISSN: 0895-4801,1095-7146
DOI: 10.1137/19m1299876