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Open AccessArticle

The Regularity of Edge Rings and Matching Numbers

1
Fachbereich Mathematik, Universität Duisburg-Essen, Campus Essen, 45117 Essen, Germany
2
Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Suita, Osaka 565-0871, Japan
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(1), 39; https://doi.org/10.3390/math8010039
Received: 30 November 2019 / Revised: 18 December 2019 / Accepted: 18 December 2019 / Published: 1 January 2020
(This article belongs to the Special Issue Current Trends on Monomial and Binomial Ideals)
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. View Full-Text
Keywords: edge ring; edge polytope; regularity; matching number edge ring; edge polytope; regularity; matching number
MDPI and ACS Style

Herzog, J.; Hibi, T. The Regularity of Edge Rings and Matching Numbers. Mathematics 2020, 8, 39.

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