PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

On total chromatic number of direct product graphs
Blaž Zmazek and Katja Prnaver
In: Seventh Cologne-Twente Workshop on Graphs and Combinatorial Optimization, 13-15 May 2008, Italy.

Abstract

The Total Coloring Conjecture (TCC), posed independently by Behzad and Vizing, states that every simple graph G has χ′′(G) ≤ ¢(G) + 2. If χ′′(G) = ¢(G) + 1, then G is a type 1 graph; if χ′′(G) = ¢(G) + 2, then G is a type 2 graph. The TCC has been confirmed for cartesian product of graphs G and H, if the TCC holds for the graphs G and H by Zmazek, Zerovnik and for the powers of cycles Ckk by Campos, Mello [5].Here we confirm the TCC for direct product of a path, Pn, and a graph G, where G is type 1 graph. We further investigate the total chromatic number of direct product of a path and an arbitrary cycle.

EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:4614
Deposited By:Igor Pesek
Deposited On:13 March 2009