Saha, KamaleshKamaleshSahaSengupta, IndranathIndranathSengupta2025-09-172025-09-172025-09-0110.1142/S100538672500032X2-s2.0-105014466641https://d8.irins.org/handle/IITG2025/32762Let 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 graph theory as well as in molecular biology, 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-completions 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 this class, we give a polynomial-time algorithm to compute the CCM-completion number and a minimum CCM-completion of a given graph. The unmixedness and Cohen-Macaulay properties of binomial edge ideals of induced subgraphs are investigated. Also, we discuss the accessible graph completion and the Cohen-Macaulay property of binomial edge ideals of whisker graphs.falsebinomial edge ideals | closed graphs | Cohen-Macaulayness | completion | unmixednessJournal02191733443-4601 September 20250arArticleWOS:001560559200007