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arXiv · 1905.02640

Induced matchings in strongly biconvex graphs and some algebraic applications

Sara Saeedi Madani·Dariush Kiani
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Abstract

In this paper, motivated by a question posed in \cite{AH}, we introduce strongly biconvex graphs as a subclass of weakly chordal and bipartite graphs. We give a linear time algorithm to find an induced matching for such graphs and we prove that this algorithm indeed gives a maximum induced matching. Applying this algorithm, we provide a strongly biconvex graph whose (monomial) edge ideal does not admit a unique extremal Betti number. Using this constructed graph, we provide an infinite family of the so-called closed graphs (also known as proper interval graphs) whose binomial edge ideals do not have a unique extremal Betti number. This, in particular, answers the aforementioned question in \cite{AH}.

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Sara Saeedi Madani, Dariush Kiani. 2019-05-07. Induced matchings in strongly biconvex graphs and some algebraic applications. https://arxiv.org/abs/1905.02640

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