Partitioning 3-edge-colored complete equi-bipartite graphs by monochromatic trees under a color degree condition
| dc.creator | Li, Xueliang | |
| dc.creator | Liu, Fengxia | |
| dc.date | 2008-01-01 | |
| dc.date | 2008-01-03 | |
| dc.date.accessioned | 2026-07-07T08:52:03Z | |
| dc.date.available | 2026-07-07T08:52:03Z | |
| dc.description | 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 $t_2(K(n_1,n_2,...,n_k))$. 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 $t_3(K(n,n))=3.$ | |
| dc.description | 16 pages | |
| dc.identifier | https://arxiv.org/abs/0801.0270 | |
| dc.identifier | http://arxiv.org/abs/0801.0270 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/145151 | |
| dc.subject | Combinatorics | |
| dc.subject | 05C70; 05C35; 05C05; 05C15 | |
| dc.title | Partitioning 3-edge-colored complete equi-bipartite graphs by monochromatic trees under a color degree condition | |
| dc.type | text |