\((2,k)\)-factor-critical graphs and toughness
type: Item
instance of: scholarly article
title: \((2,k)\)-factor-critical graphs and toughness
zbMATH Open document ID: 0930.05076
author: Odile Favaron
author: Hao Li
author: Mao-Cheng Cai
published in: Graphs and Combinatorics
publication date: 2000-02-09T00:00:00Z
review text: A graph \(G\) is \((r,k)\)-factor-critical if \(G-W\) has an \(r\)-factor for every \(W\subseteq V(G)\) with \(|W|= k\). It is shown that every \(\tau\)-tough graph of order \(n\) with \(\tau\geq 2\) is \((2,k)\)-factor-critical for every nonnegative integer \(k\leq \min\{2\tau-2, n- 3\}\). This settles a conjecture of Liu and Yu.
Mathematics Subject Classification ID: 05C70
Mathematics Subject Classification ID: 05C40
zbMATH DE Number: 1332847
zbMATH Keywords: toughness
zbMATH Keywords: factorization
zbMATH Keywords: factors
zbMATH Keywords: matchings
reviewed by: G. Gutin
MaRDI profile type: Publication
full work available at URL: s003730050035
OpenAlex ID: W2915117831
DOI: 10.1007/S003730050035
description: scientific article; zbMATH DE number 1332847