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

Katsuhiro Ota, Taro Tokuda

Research output: Contribution to journalArticle

15 Citations (Scopus)

### Abstract

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 language English 59-64 6 Journal of Graph Theory 22 1 Published - 1996 May

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Degree Condition
Minimum Degree
Induced Subgraph
Connected graph
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Integer
Graph in graph theory

### ASJC Scopus subject areas

• Mathematics(all)

### Cite this

In: Journal of Graph Theory, Vol. 22, No. 1, 05.1996, p. 59-64.

Research output: Contribution to journalArticle

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