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A Characterization of Graphs without Even Factors

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Abstract

In this paper, we first reduce the problem of finding a minimum parity (g,f)-factor of a graph G into the problem of finding a minimum perfect matching in a weighted simple graph G*. Using the structure of G*, a necessary and sufficient condition for the existence of an even factor is derived.

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Authors and Affiliations

  1. Center for Combinatorics, Nankai University Tianjin, 300071, People's Republic of China

    Xueliang Li

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

    Zhao Zhang

Authors
  1. Xueliang Li
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  2. Zhao Zhang
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Corresponding author

Correspondence to Zhao Zhang.

Additional information

This paper was accomplished while the second author was visiting the Center for Combinatorics, Nankai University.

The research is supported by NSFC

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Li, X., Zhang, Z. A Characterization of Graphs without Even Factors. Graphs and Combinatorics 22, 497–502 (2006). https://doi.org/10.1007/s00373-006-0674-z

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  • DOI: https://doi.org/10.1007/s00373-006-0674-z

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