Partially supported by Institute for Theoretical Computer Science, project 1M0545 by Ministry of Education of the Czech Republic. Partially supported by a Czech–Slovenian bilateral project MEB 091037 and BI-CZ/10-11-004.
Star Chromatic Index
Version of Record online: 29 MAR 2012
© 2012 Wiley Periodicals, Inc.
Journal of Graph Theory
Volume 72, Issue 3, pages 313–326, March 2013
How to Cite
Dvořák, Z., Mohar, B. and Šámal, R. (2013), Star Chromatic Index. J. Graph Theory, 72: 313–326. doi: 10.1002/jgt.21644
- Issue online: 23 JAN 2013
- Version of Record online: 29 MAR 2012
- Manuscript Revised: 15 DEC 2011
- Manuscript Received: 15 NOV 2010
- graph coloring;
- edge coloring
The star chromatic index of a graph G is the minimum number of colors needed to properly color the edges of the graph so that no path or cycle of length four is bi-colored. We obtain a near-linear upper bound in terms of the maximum degree . Our best lower bound on in terms of Δ is valid for complete graphs. We also consider the special case of cubic graphs, for which we show that the star chromatic index lies between 4 and 7 and characterize the graphs attaining the lower bound. The proofs involve a variety of notions from other branches of mathematics and may therefore be of certain independent interest.