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Dominating induced matchings of finite graphs and regularity of edge ideals

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Abstract

The regularity of the edge ideal of a finite simple graph G is at least the induced matching number of G and is at most the minimum matching number of G. If G possesses a dominating induced matching, i.e. an induced matching which forms a maximal matching, then the induced matching number of G is equal to the minimum matching number of G. In the present paper, from viewpoints of both combinatorics and commutative algebra, finite simple graphs with dominating induced matchings will be mainly studied.

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Acknowledgments

The third author is partially supported by JSPS Grant-in-Aid for Young Scientists (B) 24740008. We thank the anonymous referees for reading the manuscript carefully.

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Authors and Affiliations

  1. Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Toyonaka, Osaka, 560-0043, Japan

    Takayuki Hibi & Akiyoshi Tsuchiya

  2. Department of Mathematics, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-ku, Kyoto, 603-8555, Japan

    Akihiro Higashitani

  3. Department of Mathematics, Faculty of Science, Shizuoka University, 836 Ohya, Suruga-ku, Shizuoka, 422-8529, Japan

    Kyouko Kimura

Authors
  1. Takayuki Hibi
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  2. Akihiro Higashitani
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  3. Kyouko Kimura
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  4. Akiyoshi Tsuchiya
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Correspondence to Kyouko Kimura.

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Hibi, T., Higashitani, A., Kimura, K. et al. Dominating induced matchings of finite graphs and regularity of edge ideals. J Algebr Comb 43, 173–198 (2016). https://doi.org/10.1007/s10801-015-0632-z

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  • DOI: https://doi.org/10.1007/s10801-015-0632-z

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