We prove that the acyclic chromatic index a′ (G) ≤ 6 Δ for all graphs with girth at least 9. We extend the same method to obtain a bound of 4.52 Δ with the girth requirement g ≥ 220. We also obtain a relationship between g and a′ (G). © 2007 Elsevier B.V. All rights reserved.

N. Narayanan

Department of Mathematics

Rahul Muthu

Subramanian C.R.

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IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

Journal	Discrete Mathematics
ISSN	0012365X
Open Access	No