Geodesic
Partitioning 3-edge-colored complete equi-bipartite graphs by monochromatic trees under a color degree condition
The electronic journal of combinatorics, Tome 15 (2008)

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Zbl arXiv EuDML
The monochromatic tree partition number of an $r$-edge-colored graph $G$, denoted by $t_r(G)$, 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 $t_2(K(n_1,n_2,\cdots,n_k))$. In this paper, we prove that if $n\geq 3$, and $K(n,n)$ is 3-edge-colored such that every vertex has color degree 3, then $t_3(K(n,n))=3$.
DOI : 10.37236/855
Classification : 05C05, 05C15, 05C70, 05C35
Mots-clés : monochromatic tree partition, edge colored graph, verwx disjoint monochromatic trees, vertex covering, multipartite graph 
Xueliang Li; Fengxia Liu. Partitioning 3-edge-colored complete equi-bipartite graphs by monochromatic trees under a color degree condition. The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/855
@article{10_37236_855,
     author = {Xueliang Li and Fengxia Liu},
     title = {Partitioning 3-edge-colored complete equi-bipartite graphs by monochromatic trees under a color degree condition},
     journal = {The electronic journal of combinatorics},
     year = {2008},
     volume = {15},
     doi = {10.37236/855},
     zbl = {1165.05319},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/855/}
}
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