Optimal acyclic edge colouring of grid like graphs

Authors:
Rahul Muthu;N. Narayanan;C. R. Subramanian
Affiliations:
The Institute of Mathematical Sciences, Chennai, India;The Institute of Mathematical Sciences, Chennai, India;The Institute of Mathematical Sciences, Chennai, India
Venue:
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
Year:
2006

Citing 6
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Abstract

We determine the values of the acyclic chromatic index of a class of graphs referred to as d-dimensional partial tori. These are graphs which can be expressed as the Cartesian product of d graphs each of which is an induced path or cycle. This class includes some known classes of graphs like d-dimensional meshes (hypergrids), hypercubes, tori, etc. Our estimates are exact except when the graph is a product of a path and a number of odd cycles, in which case the estimates differ by an additive factor of at most 1. Our results are also constructive and provide an optimal (or almost optimal) acyclic edge colouring in polynomial time.