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Partitioning 2-edge-colored complete multipartite graphs into monochromatic cycles, paths and trees

Author

Listed:
  • Zemin Jin

    (Nankai University
    Zhejiang Normal University)

  • Mikio Kano

    (Ibaraki University)

  • Xueliang Li

    (Nankai University)

  • Bing Wei

    (University of Mississippi)

Abstract

In this paper we consider the problem of partitioning complete multipartite graphs with edges colored by 2 colors into the minimum number of vertex disjoint monochromatic cycles, paths and trees, respectively. For general graphs we simply address the decision version of these three problems the 2-PGMC, 2-PGMP and 2-PGMT problems, respectively. We show that both 2-PGMC and 2-PGMP problems are NP-complete for complete multipartite graphs and the 2-PGMT problem is NP-complete for bipartite graphs. This also implies that all these three problems are NP-complete for general graphs, which solves a question proposed by the authors in a previous paper. Nevertheless, we show that the 2-PGMT problem can be solved in polynomial time for complete multipartite graphs.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:11:y:2006:i:4:d:10.1007_s10878-006-8460-7
    DOI: 10.1007/s10878-006-8460-7
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    Cited by:

    1. 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.

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