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On Cartesian Product of Factor-Critical Graphs

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Abstract

A graph G is k-factor-critical if G − S has a perfect matching for any k-subset S of V(G). In this paper, we investigate the factor-criticality in Cartesian products of graphs and show that Cartesian product of an m-factor-critical graph and an n-factor-critical graph is \({(m+n+\varepsilon )}\) -factor-critical, where \({\varepsilon = 0}\) if both of m and n are even; \({\varepsilon = 1}\) , otherwise. Moreover, this result is best possible.

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References

  1. Bondy J.A., Murty U.S.R.: Graph Theory, GTM-244, Springer, Berlin (2008)

  2. Favaron O.: On k-factor-critical graphs. Discuss. Math. Graph Theory 16, 41–51 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  3. Győri E., Plummer M.D.: The Cartesian Product of a k-extendable and an l-extendable graph is (k + l + 1)−extendable. Discret. Math. 101, 87–96 (1992)

    Article  Google Scholar 

  4. Győri E., Imrich W.: On the strong product of a k-extendable and an l-extendable graph. Graphs Combin. 17, 245–253 (2001)

    Article  MathSciNet  Google Scholar 

  5. Imrich W., Klavžar S.: Product Graphs, Structure and Recognition. Wiley, New York

  6. Liu J.P., Yu Q.L.: Matching extensions and products of graphs. Ann. Discret. Math. 55, 191–200 (1993)

    Article  MathSciNet  Google Scholar 

  7. Lovász L., Plummer M.D.: Matching Theory. North-Holland Inc., Amsterdam (1986)

    MATH  Google Scholar 

  8. Yu Q.L.: Characterizations of various matching extensions in graphs. Australas. J. Combin. 7, 55–64 (1993)

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Center for Combinatorics, LPMC, Nankai University, Tianjin, China

    Zefang Wu & Xu Yang

  2. Department of Mathematics and Statistics, Thompson Rivers University, Kamloops, BC, Canada

    Qinglin Yu

Authors
  1. Zefang Wu
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  2. Xu Yang
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  3. Qinglin Yu
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Corresponding author

Correspondence to Qinglin Yu.

Additional information

This work is supported by Discovery Grant (114073) of Natural Sciences and Engineering Research Council of Canada.

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Wu, Z., Yang, X. & Yu, Q. On Cartesian Product of Factor-Critical Graphs. Graphs and Combinatorics 28, 723–736 (2012). https://doi.org/10.1007/s00373-011-1072-8

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  • DOI: https://doi.org/10.1007/s00373-011-1072-8

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