### Abstract

This paper contains two principal results. The first proves that any graph G can be given a balanced proper edge coloring by k colors for any k ≥ χ′ (G). Here balanced means that the number of vertices incident with any set of d colors is essentially fixed for each d, that is, for two different d-sets of colors the number of vertices incident with each of them can differ by at most 2. The second result gives upper bounds for the vertex-distinguishing edge chromatic number of graphs G with few vertices of low degree. In particular, it proves a conjecture of Burris and Schelp in the case when Δ(G) ≥ 2 V(G) + 4 and δ(G) ≥ 5.

Original language | English (US) |
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Pages (from-to) | 3-20 |

Number of pages | 18 |

Journal | Journal of Combinatorial Theory. Series B |

Volume | 90 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2004 |

Externally published | Yes |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics

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## Cite this

Balister, P. N., Kostochka, A., Li, H., & Schelp, R. H. (2004). Balanced edge colorings.

*Journal of Combinatorial Theory. Series B*,*90*(1), 3-20. https://doi.org/10.1016/S0095-8956(03)00073-X