Existence of 3-factors in k1,n-free graphs with connectivity and edge-connectivity conditions

Keiko Kotani, Shuto Nishida

Research output: Contribution to journalArticlepeer-review

Abstract

Let t be an integer satisfying t ≥ 5. We show that if G is a ⌈(t − 1)/3⌉-connected K1,t-free graph of even order with minimum degree at least ⌈(4t − 1)/3⌉, then G has a 3-factor, and if G is a ⌈(4t − 4)/3⌉-connected K1,t-free graph of even order, then G has a 3-factor. We also show that if G is a 2-edge-connected K1,4-free graph of even order with minimum degree at least 6, then G has a 3-factor.

Original languageEnglish
Pages (from-to)106-122
Number of pages17
JournalAustralasian Journal of Combinatorics
Volume79
Publication statusPublished - 2021

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