Translator Disclaimer
2019 Prime graphs, matchings and the Castelnuovo-Mumford regularity
Turker Biyikouglu, Yusuf Civan
J. Commut. Algebra 11(1): 1-27 (2019). DOI: 10.1216/JCA-2019-11-1-1

Abstract

We demonstrate the effectiveness of prime graphs for the calculation of the (Castelnuovo-Mumford) regularity of graphs. Such a notion allows us to reformulate the regularity as a generalized induced matching problem and perform regularity calculations in specific graph classes, including $(C_3,P_5)$-free graphs, $P_6$-free bipartite graphs and all Cohen-Macaulay graphs of girth at least five. In particular, we verify that the five cycle graph $C_5$ is the unique connected graph satisfying the inequality $im (G)\lt \mbox {reg}(G)=m (G)$. In addition, we prove that, for each integer $n\geq 1$, there exists a vertex decomposable perfect prime graph $G_n$ with $\mbox {reg}(G_n)=n$.

Citation

Download Citation

Turker Biyikouglu. Yusuf Civan. "Prime graphs, matchings and the Castelnuovo-Mumford regularity." J. Commut. Algebra 11 (1) 1 - 27, 2019. https://doi.org/10.1216/JCA-2019-11-1-1

Information

Published: 2019
First available in Project Euclid: 13 March 2019

zbMATH: 07037586
MathSciNet: MR3922424
Digital Object Identifier: 10.1216/JCA-2019-11-1-1

Subjects:
Primary: 05C70 , 05C75 , 05C76 , 05E40 , 13F55

Keywords: (Castelnuovo-Mumford) regularity , Cohen-Macaulay graph , Edge ideal , induced matching number , matching number , prime graph

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

JOURNAL ARTICLE
27 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.11 • No. 1 • 2019
Back to Top