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Horizons in Combinatorics/16th Shanks Lecture Series
May 21-24, 2001
Vanderbilt University
Nashville, TN, USA

Organizers
Paul Edelman, Mark Ellingham, Jonathan Farley, Mike Plummer, Jerry Spinrad

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Partitioning Multipartite Complete Graphs by Monochromatic Trees
by
Atsushi Kaneko
Kogakuin University
Coauthors: M.Kano (Ibaraki University), Kazuhiro Suzuki(Kogakuin University)

The tree partition number of r-edge-colored graph G is defined to be the minimum number 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. We determine the tree partition number of 2-edge-colored complete multipartite graphs. In particular, we prove that the tree partition number of 2-edge-colored complete bipartite graph K(n, m)  (2 <= n <= m) is ë (m-2)/2n û + 2.

Date received: April 19, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # cags-44.