Large Monochromatic Components in Edge Colored Graphs with a Minimum Degree Condition
نویسندگان
چکیده
منابع مشابه
Large Monochromatic Components in Edge Colored Graphs with a Minimum Degree Condition
It is well-known that in every k-coloring of the edges of the complete graph Kn there is a monochromatic connected component of order at least n k−1 . In this paper we study an extension of this problem by replacing complete graphs by graphs of large minimum degree. For k = 2 the authors proved that δ(G) > 3n 4 ensures a monochromatic connected component with at least δ(G) + 1 vertices in every...
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The monochromatic tree partition number of an r-edge-colored graph G, denoted by tr(G), is the minimum integer k such that whenever the edges of G are colored with r colors, the vertices of G can be covered by at most k vertex-disjoint monochromatic trees. In general, to determine this number is very difficult. For 2edge-colored complete multipartite graph, Kaneko, Kano, and Suzuki gave the exa...
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In this article we study the monochromatic cycle partition problem for non-complete graphs. We consider graphs with a given independence number (G)= . Generalizing a classical conjecture of Erd” os, Gyárfás and Pyber, we conjecture that if we r -color the edges of a graph G with (G)= , then the vertex set of G can be partitioned into at most r vertex disjoint monochromatic cycles. In the direct...
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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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Let G = (V,E) be an edge-colored graph, i.e., G is assigned a surjective function C : E → {1, 2, · · · , r}, the set of colors. A matching of G is called heterochromatic if its any two edges have different colors. Let (B,C) be an edge-colored bipartite graph and d(v) be color degree of a vertex v. We show that if d(v) ≥ k for every vertex v of B, then B has a heterochromatic matching of cardina...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2017
ISSN: 1077-8926
DOI: 10.37236/7049