Contract grant sponsor: NSFC; Contract grant numbers: 11071223; 61170302; Contract grant sponsor: ZJNSFC; Contract grant number: Z6090150; Contract grant sponsor: ZJIP; Contract grant number: T200905; Contract grant sponsors: ZSDZZZZXK13; IP-OCNS-ZJNU.
Acyclic Chromatic Indices of Planar Graphs with Girth At Least 4
Article first published online: 11 JUL 2012
© 2012 Wiley Periodicals, Inc.
Journal of Graph Theory
Volume 73, Issue 4, pages 386–399, August 2013
How to Cite
Shu, Q., Wang, W. and Wang, Y. (2013), Acyclic Chromatic Indices of Planar Graphs with Girth At Least 4. J. Graph Theory, 73: 386–399. doi: 10.1002/jgt.21683
- Issue published online: 4 JUN 2013
- Article first published online: 11 JUL 2012
- Manuscript Revised: 4 MAY 2012
- Manuscript Received: 25 NOV 2010
- NSFC. Grant Numbers: 11071223, 61170302
- ZJNSFC. Grant Number: Z6090150
- ZJIP. Grant Number: T200905
- ZSDZZZZXK13; IP-OCNS-ZJNU
- acyclic edge coloring;
- planar graph;
- maximum degree
An acyclic edge coloring of a graph G is a proper edge coloring such that no bichromatic cycles are produced. The acyclic chromatic index of G is the smallest integer k such that G has an acyclic edge coloring using k colors. Fiamik (Math. Slovaca 28 (1978), 139–145) and later Alon et al. (J Graph Theory 37 (2001), 157–167) conjectured that for any simple graph G with maximum degree Δ. In this article, we confirm this conjecture for planar graphs of girth at least 4.