### Abstract

Let d, k be any two positive integers with k > d > 0. We consider a k-coloring of a graph G such that the distance between each pair of vertices in the same color-class is at least d. Such graphs are said to be (k,d)-colorable. The object of this paper is to determine the maximum size of (k,3)-colorable, (k,4)-colorable, and (k,k-1)-colorable graphs. Sharp results are obtained for both (k,3)-colorable and (k,k-1)-colorable graphs, while the results obtained for (k,4)-colorable graphs are close to the truth.

Original language | English |
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Pages (from-to) | 65-82 |

Number of pages | 18 |

Journal | Discrete Mathematics |

Volume | 191 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - Sep 28 1998 |

### Keywords

- Chromatic number
- Coloring
- Distance
- Extremal number

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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## Cite this

Chen, G., Gyárfás, A., & Schelp, R. H. (1998). Vertex colorings with a distance restriction.

*Discrete Mathematics*,*191*(1-3), 65-82. https://doi.org/10.1016/S0012-365X(98)00094-6