Analysis of a heuristic for acyclic edge colouring

Authors:
C. R. Subramanian
Affiliations:
The Institute of Mathematical Sciences, Chennai, India
Venue:
Information Processing Letters
Year:
2006

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Abstract

An acyclic edge colouring of a graph is a proper edge colouring in which the union of any two colour classes does not contain a cycle, that is, forms a forest. It is known that there exists such a colouring using at most 16Δ(G) colours where Δ(G) denotes the maximum degree of a graph G. However, no non-trivial constructive bound (which works for all graphs) is known except for the straightforward distance 2 colouring which requires Δ2 colours. We analyse a simple O(mnΔ2(log Δ)2) time greedy heuristic and show that it uses at most 5Δ(log Δ + 2) colours on any graph.