Acyclic Chromatic Indices of Planar Graphs with Girth At Least 4 |
| |
| Authors: | Qiaojun Shu Weifan Wang Yiqiao Wang |
| |
| Affiliation: | 1. DEPARTMENT OF MATHEMATICS, ZHEJIANG NORMAL UNIVERSITY, , 321004 JINHUA, CHINA;2. SCHOOL OF HEALTH MANAGEMENT, BEIJING UNIVERSITY OF CHINESE MEDICINE, , 100029 BEIJING, CHINA |
| |
| Abstract: | 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. Fiam ik (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. |
| |
| Keywords: | acyclic edge coloring planar graph girth maximum degree |
|
|
