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Path-Factors in the Square of a Tree

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Abstract

In this paper, we give a necessary condition for the existence of P 3-factor in the square of a tree. Furthermore, we show that the square of any tree on at least 6 vertices has a {P 3,P 4}-factor. As a consequence, every connected graph on at least 6 vertices has a {P 3,P 4}-factor.

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Authors and Affiliations

  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang, 830046, People’s Republic of China

    Xiaojuan Li & Zhao Zhang

Authors
  1. Xiaojuan Li
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  2. Zhao Zhang
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Corresponding author

Correspondence to Zhao Zhang.

Additional information

Zhao Zhang: The research is supported by NSFC (60603003) and XJEDU.

Received: November 15, 2006. Final version received: December 12, 2007.

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Li, X., Zhang, Z. Path-Factors in the Square of a Tree. Graphs and Combinatorics 24, 107–111 (2008). https://doi.org/10.1007/s00373-008-0775-y

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  • DOI: https://doi.org/10.1007/s00373-008-0775-y

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