(2,k)-Factor-Critical Graphs and Toughness

descriptionPublicationkeyboard_double_arrow_right Article 15 Jun 1999Publisher:Springer Science and Business Media LLCJournal:Graphs and Combinatorics, volume 15, pages 137-142 (issn: 0911-0119, eissn: 1435-5914,

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Authors: Mao-cheng Cai; Odile Favaron; Hao Li 0002;

doi: 10.1007/s003730050035

(2,k)-Factor-Critical Graphs and Toughness

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Abstract

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.

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Keywords

Connectivity, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), factorization, factors, toughness, matchings

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