On monochromatic subgraphs of edge-colored complete graphs
نویسندگان
چکیده
منابع مشابه
On monochromatic subgraphs of edge-colored complete graphs
In a red-blue coloring of a nonempty graph, every edge is colored red or blue. If the resulting edge-colored graph contains a nonempty subgraph G without isolated vertices every edge of which is colored the same, then G is said to be monochromatic. For two nonempty graphs G and H without isolated vertices, the monochromatic Ramsey number mr(G,H) of G and H is the minimum integer n such that eve...
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Lehel conjectured that for all n, any 2-edge-coloring of Kn admits a partition of the vertex set into a red cycle and a blue cycle. This conjecture led to a significant amount of work on related questions and was eventually proven for all n by Bessy and Thomassé. Balogh, Barát, Gerbner, Gyárfás, and Sárközy conjectured a stronger statement for large n: that if δ(G) > 3n/4, then any 2-edge-color...
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Nowadays the term monochromatic and heterochromatic (or rainbow, multicolored) subgraphs of an edge colored graph appeared frequently in literature, and many results on this topic have been obtained. In this paper, we survey results on this subject. We classify the results into the following categories: vertex-partitions by monochromatic subgraphs, such as cycles, paths, trees; vertex partition...
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Consider edge-colorings of the complete graph Kn. Let r(n, t) be the maximum number of colors in such a coloring that does not have t edge-disjoint rainbow spanning trees. Let s(n, t) be the maximum number of colors in such a coloring having no rainbow spanning subgraph with diameter at most t. We prove r(n, t) = (n−2 2 )
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2014
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.1725