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 graph theory as w...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 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.展开更多
We study the projective closures of three important families of affine monomial curves in dimension 4,namely the Backelin curve,the Bresinsky curve and the Arslan curve,in order to explore possible connections between...We study the projective closures of three important families of affine monomial curves in dimension 4,namely the Backelin curve,the Bresinsky curve and the Arslan curve,in order to explore possible connections between syzygies and the arithmetic Cohen-Macaulay property.展开更多
We find an explicit expression of the associated primes of monomial ideals as a colon by an element,using the unique irredundant irreducible decomposition whose irreducible components are monomial ideals.An algorithm ...We find an explicit expression of the associated primes of monomial ideals as a colon by an element,using the unique irredundant irreducible decomposition whose irreducible components are monomial ideals.An algorithm to compute is given using Macaulay2.For squarefree monomial ideals the problem is related to the combinatorics of the underlying clutter or graph.For ideals of Borel type,the monomial u takes a simpler form,and we classify when is unique.展开更多
文摘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 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.
文摘We study the projective closures of three important families of affine monomial curves in dimension 4,namely the Backelin curve,the Bresinsky curve and the Arslan curve,in order to explore possible connections between syzygies and the arithmetic Cohen-Macaulay property.
基金Supported by the MATRICS research grant MTR/2018/000420sponsored by the SERB Government of India.
文摘We find an explicit expression of the associated primes of monomial ideals as a colon by an element,using the unique irredundant irreducible decomposition whose irreducible components are monomial ideals.An algorithm to compute is given using Macaulay2.For squarefree monomial ideals the problem is related to the combinatorics of the underlying clutter or graph.For ideals of Borel type,the monomial u takes a simpler form,and we classify when is unique.
