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Heterochromatic tree partition number in complete multipartite graphs

Author

Listed:
  • Zemin Jin

    (Zhejiang Normal University)

  • Peipei Zhu

    (Zhejiang Normal University)

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.

Suggested Citation

  • Zemin Jin & Peipei Zhu, 2014. "Heterochromatic tree partition number in complete multipartite graphs," Journal of Combinatorial Optimization, Springer, vol. 28(2), pages 321-340, August.
    • Handle: RePEc:spr:jcomop:v:28:y:2014:i:2:d:10.1007_s10878-012-9557-9
    DOI: 10.1007/s10878-012-9557-9
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    References listed on IDEAS

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    1. Zemin Jin & Mikio Kano & Xueliang Li & Bing Wei, 2006. "Partitioning 2-edge-colored complete multipartite graphs into monochromatic cycles, paths and trees," Journal of Combinatorial Optimization, Springer, vol. 11(4), pages 445-454, June.
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