### Abstract

Let G be a graph, m>r≥1 integers. Suppose that it has a good coloring with m colors which uses at most r colors in the neighborhood of every vertex. We investigate these so-called local r-colorings. One of our results (Theorem 2.4) states: The chromatic number of G, Chr(G)≤r2^{r}log_{2}log_{2} m (and this value is the best possible in a certain sense). We consider infinite graphs as well.

Original language | English |
---|---|

Pages (from-to) | 21-34 |

Number of pages | 14 |

Journal | Discrete Mathematics |

Volume | 59 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 1986 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*59*(1-2), 21-34. https://doi.org/10.1016/0012-365X(86)90065-8

**Coloring graphs with locally few colors.** / Erdős, P.; Füredi, Z.; Hajnal, A.; Komjáth, P.; Rödl, V.; Seress, Á.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 59, no. 1-2, pp. 21-34. https://doi.org/10.1016/0012-365X(86)90065-8

}

TY - JOUR

T1 - Coloring graphs with locally few colors

AU - Erdős, P.

AU - Füredi, Z.

AU - Hajnal, A.

AU - Komjáth, P.

AU - Rödl, V.

AU - Seress, Á

PY - 1986

Y1 - 1986

N2 - Let G be a graph, m>r≥1 integers. Suppose that it has a good coloring with m colors which uses at most r colors in the neighborhood of every vertex. We investigate these so-called local r-colorings. One of our results (Theorem 2.4) states: The chromatic number of G, Chr(G)≤r2rlog2log2 m (and this value is the best possible in a certain sense). We consider infinite graphs as well.

AB - Let G be a graph, m>r≥1 integers. Suppose that it has a good coloring with m colors which uses at most r colors in the neighborhood of every vertex. We investigate these so-called local r-colorings. One of our results (Theorem 2.4) states: The chromatic number of G, Chr(G)≤r2rlog2log2 m (and this value is the best possible in a certain sense). We consider infinite graphs as well.

UR - http://www.scopus.com/inward/record.url?scp=38249043037&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38249043037&partnerID=8YFLogxK

U2 - 10.1016/0012-365X(86)90065-8

DO - 10.1016/0012-365X(86)90065-8

M3 - Article

VL - 59

SP - 21

EP - 34

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-2

ER -