# Improved upper bounds on acyclic edge colorings

Improved upper bounds on acyclic edge colorings An acyclic edge coloring of a graph is a proper edge coloring such that every cycle contains edges of at least three distinct colors. The acyclic chromatic index of a graph G, denoted by a′(G), is the minimum number k such that there is an acyclic edge coloring using k colors. It is known that a′(G) ≤ 16Δ for every graph G where Δ denotes the maximum degree of G. We prove that a′(G) < 13.8Δ for an arbitrary graph G. We also reduce the upper bounds of a′(G) to 9.8Δ and 9Δ with girth 5 and 7, respectively. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

# Improved upper bounds on acyclic edge colorings

, Volume 30 (2) – Apr 17, 2014
4 pages

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Publisher
Springer Journals
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-014-0293-z
Publisher site
See Article on Publisher Site

### Abstract

An acyclic edge coloring of a graph is a proper edge coloring such that every cycle contains edges of at least three distinct colors. The acyclic chromatic index of a graph G, denoted by a′(G), is the minimum number k such that there is an acyclic edge coloring using k colors. It is known that a′(G) ≤ 16Δ for every graph G where Δ denotes the maximum degree of G. We prove that a′(G) < 13.8Δ for an arbitrary graph G. We also reduce the upper bounds of a′(G) to 9.8Δ and 9Δ with girth 5 and 7, respectively.

### Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Apr 17, 2014

### References

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