Scholarlink

<p>We associate with every graph a linear program for packings of vertex disjoint paths. We show that the optimal primal and dual values of the corresponding integer program are the binomial grade and height of the binomial edge ideal of the graph. We deduce from this a new combinatorial characterization of graphs of König type and use it to show that all trees are of König type. The log canonical threshold and the F-threshold are important invariants associated with the singularities of a variety in characteristic 0 and characteristic <i>p</i>. We show that the optimal value of the linear program (computed over the rationals) agrees with both the F-threshold and the log canonical threshold of the binomial edge ideal if the graph is a block graph or of König type. We conjecture that this linear program computes the log canonical threshold of the binomial edge ideal of any graph. Our results resemble theorems on monomial ideals arising from hypergraphs due to Howald and others.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Invariants of binomial edge ideals via linear programs

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年7月15日

查看全文
  • Adam LaClair

摘要

We associate with every graph a linear program for packings of vertex disjoint paths. We show that the optimal primal and dual values of the corresponding integer program are the binomial grade and height of the binomial edge ideal of the graph. We deduce from this a new combinatorial characterization of graphs of König type and use it to show that all trees are of König type. The log canonical threshold and the F-threshold are important invariants associated with the singularities of a variety in characteristic 0 and characteristic p. We show that the optimal value of the linear program (computed over the rationals) agrees with both the F-threshold and the log canonical threshold of the binomial edge ideal if the graph is a block graph or of König type. We conjecture that this linear program computes the log canonical threshold of the binomial edge ideal of any graph. Our results resemble theorems on monomial ideals arising from hypergraphs due to Howald and others.