Heterochromatic tree partition number in complete multipartite graphs

Zemin Jin () and Peipei Zhu ()
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Zemin Jin: Zhejiang Normal University
Peipei Zhu: Zhejiang Normal University

Journal of Combinatorial Optimization, 2014, vol. 28, issue 2, No 1, 340 pages

Abstract: Abstract The heterochromatic tree partition number of an $$r$$ -edge-colored graph $$G,$$ denoted by $$t_r(G),$$ is the minimum positive integer $$p$$ such that whenever the edges of the graph $$G$$ are colored with $$r$$ colors, the vertices of $$G$$ can be covered by at most $$p$$ vertex disjoint heterochromatic trees. In this article we determine the upper and lower bounds for the heterochromatic tree partition number $$t_r(K_{n_1,n_2,\ldots ,n_k})$$ of an $$r$$ -edge-colored complete $$k$$ -partite graph $$K_{n_1,n_2,\ldots ,n_k}$$ , and the gap between upper and lower bounds is at most one.

Keywords: Monochromatic tree; Heterochromatic tree; Partition (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10878-012-9557-9

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