### Abstract

A graph is called K_{1}, _{n}-free if it contains no K_{1}, _{n} as an induced subgraph. Let n(≥ 3), r be integers (if r is odd, r ≥ n - 1). We prove that every K_{1}, _{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 |
---|---|

Pages (from-to) | 59-64 |

Number of pages | 6 |

Journal | Journal of Graph Theory |

Volume | 22 |

Issue number | 1 |

Publication status | Published - 1996 May |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

_{1},

_{n}-Free Graphs.

*Journal of Graph Theory*,

*22*(1), 59-64.

**A Degree Condition for the Existence of Regular Factors in K _{1}, _{n}-Free Graphs.** / Ota, Katsuhiro; Tokuda, Taro.

Research output: Contribution to journal › Article

_{1},

_{n}-Free Graphs',

*Journal of Graph Theory*, vol. 22, no. 1, pp. 59-64.

_{1},

_{n}-Free Graphs. Journal of Graph Theory. 1996 May;22(1):59-64.

}

TY - JOUR

T1 - A Degree Condition for the Existence of Regular Factors in K1, n-Free Graphs

AU - Ota, Katsuhiro

AU - Tokuda, Taro

PY - 1996/5

Y1 - 1996/5

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0030551098&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030551098&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0030551098

VL - 22

SP - 59

EP - 64

JO - Journal of Graph Theory

JF - Journal of Graph Theory

SN - 0364-9024

IS - 1

ER -