Monochromatic subgraphs in randomly colored graphons
نویسندگان
چکیده
منابع مشابه
Monochromatic subgraphs of 2-edge-colored graphs
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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LetKn be the complete graph with n vertices and c1, c2, · · · , cr be r different colors. Suppose we randomly and uniformly color the edges of Kn in c1, c2, · · · , cr. Then we get a random graph, denoted by K r n. In the paper, we investigate the asymptotic properties of several kinds of monochromatic and heterochromatic subgraphs in K n. Accurate threshold functions in some cases are also obt...
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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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We conjecture that for n> 4(k−1) every 2-coloring of the edges of the complete graphKn contains a k-connectedmonochromatic subgraph with at least n − 2(k − 1) vertices. This conjecture, if true, is best possible. Here we prove it for k = 2, and show how to reduce it to the case n< 7k − 6. We prove the following result as well: for n> 16k every 2-colored Kn contains a k-connected monochromatic s...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2019
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2019.06.007