Monochromatic Tree Partition for Complete Multipartite Graphs
نویسندگان
چکیده
An r-edge-coloring of a graph G is a surjective assignment of r colors to the edges of G. The monochromatic tree partition number of an redge-colored graph G is defined to be the minimum positive 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 this paper, we give a direct proof for the monochromatic tree partition number of an r-edge-colored complete multipartite graph Kn1,n2,··· ,nk . Mathematics Subject Classification: 05C35
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