### 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 |

Publication status | Published - Sep 28 1998 |

### Fingerprint

### Keywords

- Chromatic number
- Coloring
- Distance
- Extremal number

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*191*(1-3), 65-82.

**Vertex colorings with a distance restriction.** / Chen, Guantao; Gyárfás, A.; Schelp, R. H.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 191, no. 1-3, pp. 65-82.

}

TY - JOUR

T1 - Vertex colorings with a distance restriction

AU - Chen, Guantao

AU - Gyárfás, A.

AU - Schelp, R. H.

PY - 1998/9/28

Y1 - 1998/9/28

N2 - 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.

AB - 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.

KW - Chromatic number

KW - Coloring

KW - Distance

KW - Extremal number

UR - http://www.scopus.com/inward/record.url?scp=0043098229&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0043098229&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0043098229

VL - 191

SP - 65

EP - 82

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -