The Regularity of Edge Rings and Matching Numbers

Jürgen Herzog and Takayuki Hibi
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Jürgen Herzog: Fachbereich Mathematik, Universität Duisburg-Essen, Campus Essen, 45117 Essen, Germany
Takayuki Hibi: Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Suita, Osaka 565-0871, Japan

Mathematics, 2020, vol. 8, issue 1, 1-4

Abstract: Let K [ G ] denote the edge ring of a finite connected simple graph G on [ d ] and mat ( G ) the matching number of G . It is shown that reg ( K [ G ] ) ≤ mat ( G ) if G is non-bipartite and K [ G ] is normal, and that reg ( K [ G ] ) ≤ mat ( G ) − 1 if G is bipartite.

Keywords: edge ring; edge polytope; regularity; matching number (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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