Dergiler / International Electronic Journal of Algebra / 2023 / Cilt: 33 - Sayı: 33

On vertex decomposability and regularity of graphs

On vertex decomposability and regularity of graphs

Amir MAFI, Dler NADERI, Parasto SOUFIVAND

Sayfa
205–212
DOI
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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.

Anahtar kelimeler: Vertex decomposable graph, edge ideal, Castelnuovo-Mumford regularity