### Abstract

Alon and Yuster [4] have proven that if a fixed graph K on g vertices is (h + 1)-colorable, then any graph G with n vertices and minimum degree at least h/h+1n contains at least (1 - ∈)n/g vertex disjoint copies of K, provided n > N(∈). It is shown here that the required minimum degree of G for this result to follow is closer to h-1/hn, provided K has a proper (h + 1)-coloring in which some of the colors occur rarely. A conjecture regarding the best possible result of this type is suggested.

Original language | English (US) |
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Pages (from-to) | 296-308 |

Number of pages | 13 |

Journal | Ars Combinatoria |

Volume | 52 |

State | Published - Jun 1 1999 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

## Fingerprint Dive into the research topics of 'Refining the graph density condition for the existence of almost K-factors'. Together they form a unique fingerprint.

## Cite this

Alon, N., & Fischer, E. (1999). Refining the graph density condition for the existence of almost K-factors.

*Ars Combinatoria*,*52*, 296-308.