Matching numbers and dimension of edge ideals

2020/01/29 by Ayana Hirano, Hirano, Ayana, Kazunori Matsuda +1 · 1 citation
Mathematics · Computer Science · #Commutative Algebra and Its Applications #Polynomial and algebraic computation #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.2001.10704

Abstract

Let G be a finite simple graph on the vertex set V(G) = \x₁, …, x_n\ and match(G), min-match(G) and ind-match(G) the matching number, minimum matching number and induced matching number of G, respectively. Let K[V(G)] = K[x₁, …, x_n] denote the polynomial ring over a field K and I(G) ⊂ K[V(G)] the edge ideal of G. The relationship between these graph-theoretic invariants and ring-theoretic invariants of the quotient ring K[V(G)]/I(G) has been studied. In the present paper, we study the relationship between match(G), min-match(G), ind-match(G) and dim K[V(G)]/I(G).

Cited by

• The vertex covers, Betti numbers and projective dimensions of perfect binary trees

Related

• Induced matching numbers of finite graphs and edge ideals
• On the three graph invariants related to matching of finite simple graphs
• On the regularity of edge ideal of graphs
• Depth, Stanley depth and regularity of ideals associated to graphs
• Induced matchings and the v-number of graded ideals