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arXiv · 1412.3881

Dominating induced matchings of finite graphs and regularity of edge ideals

Takayuki Hibi·Akihiro Higashitani·Kyouko Kimura·Akiyoshi Tsuchiya
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Abstract

The regularity of an 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 inuduced 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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Takayuki Hibi, Akihiro Higashitani, Kyouko Kimura, Akiyoshi Tsuchiya. 2014-12-12. Dominating induced matchings of finite graphs and regularity of edge ideals. https://arxiv.org/abs/1412.3881

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