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Closed Cohen-Macaulay completion of binomial edge ideals
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Closed Cohen-Macaulay completion of binomial edge ideals
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Paper
Closed Cohen-Macaulay completion of binomial edge ideals
2022
Overview
Let \\(CCM\\) denote the class of closed graphs with Cohen-Macaulay binomial edge ideals and \\(PIG\\) denote the class of proper interval graphs. Then \\(CCM PIG\\). The \\(PIG\\)-completion problem is a classical problem in molecular biology as well as in graph theory and this problem is known to be NP-hard. In this paper, we study the \\(CCM\\)-completion problem. We give a method to construct all possible \\(CCM\\)-completion of a graph. We find the \\(CCM\\)-completion number and the set of all minimal \\(CCM\\)-completions for a large class of graphs. Moreover, for that class, we give a polynomial-time algorithm to compute the \\(CCM\\)-completion number and a minimum \\(CCM\\)-completion of a given graph. We investigate unmixed and Cohen-Macaulay properties of binomial edge ideals of induced subgraphs. Also, we discuss the accessible graphs completion and the Cohen-Macaulay property of binomial edge ideals of whisker graphs.
Publisher
Cornell University Library, arXiv.org
Subject
