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Factor-Critical Graphs with Given Number of Maximum Matchings

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Abstract

A connected graph G is said to be factor-critical if G − ν has a perfect matching for every vertex ν of G. In this paper, the factor-critical graphs G with |V(G)| maximum matchings and with |V(G)| + 1 ones are characterized, respectively. From this, some special bicritical graphs are characterized.

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Authors and Affiliations

  1. School of Mathematics, South China Normal University, Guangzhou, 510631, P.R. China

    Yan Liu

  2. Academy of Mathematics and Systems Science, Chinese Academy of Science, Beijing, 100080, P.R. China

    Guiying Yan

Authors
  1. Yan Liu
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  2. Guiying Yan
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Correspondence to Yan Liu.

Additional information

This work is supported by the Ph.D. Programs Foundation of Ministry of Education of China (No.20070574006) and the NNSF(10201019) of China.

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Liu, Y., Yan, G. Factor-Critical Graphs with Given Number of Maximum Matchings. Graphs and Combinatorics 24, 563–569 (2008). https://doi.org/10.1007/s00373-008-0816-6

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  • DOI: https://doi.org/10.1007/s00373-008-0816-6

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