A Degree Condition for the Existence of Regular Factors in K1, n-Free Graphs

Katsuhiro Ota, Taro Tokuda

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A graph is called K1, n-free if it contains no K1, n as an induced subgraph. Let n(≥ 3), r be integers (if r is odd, r ≥ n - 1). We prove that every K1, n-free connected graph G with r|V(G)| even has an r-factor if its minimum degree is at least (n + n-1/r) ⌈n/2(n - 1) r⌉ - n - 1/r (⌈n/2(n - 1) r⌉)2 + n - 3. This degree condition is sharp.

Original languageEnglish
Pages (from-to)59-64
Number of pages6
JournalJournal of Graph Theory
Issue number1
Publication statusPublished - 1996 May


ASJC Scopus subject areas

  • Geometry and Topology

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