Monochromatic and heterochromatic subgraph problems in a randomly colored graph

Details Monochromatic and heterochromatic subgraph problems in a randomly colored graph Monochromatic and heterochromatic subgraph problems in a randomly colored graph

2007-11-24

arxiv.org/abs/0711.3827v1

Mathematics

Combinatorics

11 pages

Scientific paper

Let $K_n$ be the complete graph with $n$ vertices and $c_1, c_2, ..., c_r$ be $r$ different colors. Suppose we randomly and uniformly color the edges of $K_n$ in $c_1, c_2, ..., c_r$. Then we get a random graph, denoted by $\mathcal{K}_n^r$. In the paper, we investigate the asymptotic properties of several kinds of monochromatic and heterochromatic subgraphs in $\mathcal{K}_n^r$. Accurate threshold functions in some cases are also obtained.

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