1 research outputs found
Partitioning 3-edge-colored complete equi-bipartite graphs by monochromatic trees under a color degree condition
The monochromatic tree partition number of an -edge-colored graph ,
denoted by , is the minimum integer such that whenever the edges of
are colored with colors, the vertices of can be covered by at most
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 . In this
paper, we prove that if , and K(n,n) is 3-edge-colored such that every
vertex has color degree 3, then Comment: 16 page