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Partitioning complete graphs by heterochromatic trees

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Abstract

A heterochromatic tree is an edge-colored tree in which any two edges have different colors. 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 paper we determine the heterochromatic tree partition number of r-edge-colored complete graphs. We also find at most t r (K n ) vertex-disjoint heterochromatic trees to cover all the vertices in polynomial time for a given r-edge-coloring of K n .

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China

    Ze-min Jin

  2. Center for Combinatorics and LPMC, Nankai University, Tianjin, 300071, China

    Xue-liang Li

Authors
  1. Ze-min Jin
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  2. Xue-liang Li
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Correspondence to Ze-min Jin.

Additional information

Supported by the National Natural Science Foundation of China (No. 11071130 and 11101378), Zhejiang Innovation Project (Grant No. T200905) and Zhejiang Provifenincial Natural Science Foundation of China (Z6090150).

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Jin, Zm., Li, Xl. Partitioning complete graphs by heterochromatic trees. Acta Math. Appl. Sin. Engl. Ser. 28, 625–630 (2012). https://doi.org/10.1007/s10255-012-0177-z

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  • DOI: https://doi.org/10.1007/s10255-012-0177-z

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