Partitioning 3-edge-colored complete equi-bipartite graphs by monochromatic trees under a color degree condition
Abstract
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 2-edge-colored complete multipartite graph, Kaneko, Kano, and Suzuki gave the exact value of t2(K(n1,n2,...,nk)). In this paper, we prove that if n≥ 3, and K(n,n) is 3-edge-colored such that every vertex has color degree 3, then t3(K(n,n))=3.
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