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A pair of forbidden subgraphs and perfect matchings in graphs of high connectivity

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Abstract

Sumner [7] proved that every connected K 1,3-free graph of even order has a perfect matching. He also considered graphs of higher connectivity and proved that if m ≥ 2, every m-connected K 1,m+1-free graph of even order has a perfect matching. In [6], two of the present authors obtained a converse of sorts to Sumner’s result by asking what single graph one can forbid to force the existence of a perfect matching in an m-connected graph of even order and proved that a star is the only possibility. In [2], Fujita et al. extended this work by considering pairs of forbidden subgraphs which force the existence of a perfect matching in a connected graph of even order. But they did not settle the same problem for graphs of higher connectivity. In this paper, we give an answer to this problem. Together with the result in [2], a complete characterization of the pairs is given.

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Authors and Affiliations

  1. Faculty of Business and Commerce, Keio University, Hiyoshi 4-1-1, Kohoku-Ku, Yokohama, Kanagawa, 223-8521, Japan

    Jun Fujisawa

  2. Department of Mathematics, Gunma National College of Technology, 580 Toriba, Maebashi, Gunma, 371-8530, Japan

    Shinya Fujita

  3. Department of Mathematics, Vanderbilt University, Nashville, Tennessee, 37240, USA

    Michael D. Plummer

  4. Department of Computer Science, Nihon University, Sakurajosui 3-25-40, Setagaya-Ku, Tokyo, 156-8550, Japan

    Akira Saito

  5. Institut für Diskrete Mathematik und Algebra, TU Bergakademie Freiberg, 09596, Freiberg, Germany

    Ingo Schiermeyer

Authors
  1. Jun Fujisawa
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  2. Shinya Fujita
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  3. Michael D. Plummer
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  4. Akira Saito
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  5. Ingo Schiermeyer
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Corresponding author

Correspondence to Jun Fujisawa.

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Fujisawa, J., Fujita, S., Plummer, M.D. et al. A pair of forbidden subgraphs and perfect matchings in graphs of high connectivity. Combinatorica 31, 703–723 (2011). https://doi.org/10.1007/s00493-011-2655-y

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  • DOI: https://doi.org/10.1007/s00493-011-2655-y

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