On vertex decomposability and regularity of graphs

Year 2023, Volume: 33 Issue: 33, 205 - 212, 09.01.2023

Amir Mafı Dler Naderı Parasto Soufıvand

https://doi.org/10.24330/ieja.1217285

Abstract

There are two motivating questions in [M. Mahmoudi, A. Mousivand, M. Crupi, G. Rinaldo, N. Terai and S. Yassemi, arXiv:1006.1087v1] and [M. Mahmoudi, A. Mousivand, M. Crupi, G. Rinaldo, N. Terai and S. Yassemi, J. Pure Appl. Algebra, 215(10) (2011), 2473-2480] about Castelnuovo-Mumford regularity and vertex decomposability of simple graphs. In this paper, we give negative answers to the questions by providing two counterexamples.

Keywords

Vertex decomposable graph, edge ideal, Castelnuovo-Mumford regularity

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