In this paper, we study the problem of regular decomposition in integer program- ming. We apply the radical of binomial ideal and universal Grobner bases to get the regular decomposition forms of a finite integer latt...In this paper, we study the problem of regular decomposition in integer program- ming. We apply the radical of binomial ideal and universal Grobner bases to get the regular decomposition forms of a finite integer lattice point set. We indicate the relationship between state polytope and regular decompositions, i.e., an edge of state polytope corresponds to a binomial which decides one of regular decomposition forms of a finite integer lattice point set.展开更多
In this article,we obtain an upper bound for the regularity of the binomial edge ideal of a graph whose every block is either a cycle or a clique.As a consequence,we obtain an upper bound for the regularity of binomia...In this article,we obtain an upper bound for the regularity of the binomial edge ideal of a graph whose every block is either a cycle or a clique.As a consequence,we obtain an upper bound for the regularity of binomial edge ideal of a cactus graph.We also identify a certain subclass attaining the upper bound.展开更多
We provide the regularity and the Cohen-Macaulay type of binomial edge ideals of Cohen-Macaulay cones,and we show the extremal Betti numbers of some classes of Cohen-Macaulay binomial edge ideals:Cohen-Macaulay bipart...We provide the regularity and the Cohen-Macaulay type of binomial edge ideals of Cohen-Macaulay cones,and we show the extremal Betti numbers of some classes of Cohen-Macaulay binomial edge ideals:Cohen-Macaulay bipartite and fan graphs.In addition,we compute the Hilbert-Poincare series of the binomial edge ideals of some Cohen-Macaulaybipartitegraphs.展开更多
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
基金Supported by the National Natural Science Foundation of China(Grant Nos.11671068,11271060)Fundamental Research of Civil Aircraft(Grant No.MJ-F-2012-04)the Fundamental Research Funds for the Central Universities(Grant No.DUT16LK38)
文摘In this paper, we study the problem of regular decomposition in integer program- ming. We apply the radical of binomial ideal and universal Grobner bases to get the regular decomposition forms of a finite integer lattice point set. We indicate the relationship between state polytope and regular decompositions, i.e., an edge of state polytope corresponds to a binomial which decides one of regular decomposition forms of a finite integer lattice point set.
文摘In this article,we obtain an upper bound for the regularity of the binomial edge ideal of a graph whose every block is either a cycle or a clique.As a consequence,we obtain an upper bound for the regularity of binomial edge ideal of a cactus graph.We also identify a certain subclass attaining the upper bound.
基金The first author was supported by the“National Group for Algebraic and Geometric Structures,and Their Applications”(GNSAGA-INdAM).
文摘We provide the regularity and the Cohen-Macaulay type of binomial edge ideals of Cohen-Macaulay cones,and we show the extremal Betti numbers of some classes of Cohen-Macaulay binomial edge ideals:Cohen-Macaulay bipartite and fan graphs.In addition,we compute the Hilbert-Poincare series of the binomial edge ideals of some Cohen-Macaulaybipartitegraphs.
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.
