Abstract
An edge colouring ϕ of a graph G is locally irregular if each colour class of ϕ induces a graph whose every adjacent vertices have distinct degrees. The least number \( X'_{irr} (G) \) of colours used by a locally irregular edge colouring of G (if any) is referred to as the irregular chromatic index of G.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
M. Karoński, T. Luczak and A. Thomason, Edge weights and vertex colours, J. Combin. Theory, Ser, B 91(1) (2004), 151–157.
L. Addario-Berry, R. E. L. Aldred, K. Dalal and B. A. Reed, Vertex colouring edge partitions, J. Combin. Theory, Ser. B 94(2) (2005), 237–244.
O. Baudon, J. Bensmail, J. Przybyło and M. Woźniak, On decomposing regular graphs into locally irregular subgraphs, Preprint MD 065, http://www.ii.uj.edu.pl/preMD/index.php, 2013.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2013 Scuola Normale Superiore Pisa
About this paper
Cite this paper
Bensmail, J. (2013). Complexity of determining the irregular chromatic index of a graph. In: Nešetřil, J., Pellegrini, M. (eds) The Seventh European Conference on Combinatorics, Graph Theory and Applications. CRM Series, vol 16. Edizioni della Normale, Pisa. https://doi.org/10.1007/978-88-7642-475-5_104
Download citation
DOI: https://doi.org/10.1007/978-88-7642-475-5_104
Publisher Name: Edizioni della Normale, Pisa
Print ISBN: 978-88-7642-474-8
Online ISBN: 978-88-7642-475-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)