Geodesic
Dominating induced matchings of finite graphs and regularity of edge ideals
Journal of Algebraic Combinatorics, Tome 43 (2016) no. 1, pp. 173-198.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 05E40, 05C69, 05C70
Keywords: edge ideal, dominating induced matching, regularity, unmixed graph, vertex decomposable graph 
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Hibi, Takayuki; Higashitani, Akihiro; Kimura, Kyouko; Tsuchiya, Akiyoshi. Dominating induced matchings of finite graphs and regularity of edge ideals. Journal of Algebraic Combinatorics, Tome 43 (2016) no. 1, pp. 173-198. http://geodesic.mathdoc.fr/item/JAC_2016__43_1_a2/