Discussiones Mathematicae Graph Theory 29(2) (2009) 411-418
doi: 10.7151/dmgt.1456

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ON k-INTERSECTION EDGE COLOURINGS

Rahul Muthu, N. Narayanan and C.R. Subramanian

The Institute of Mathematical Sciences
Taramani, Chennai-600113, India
e-mail: {rahulm,narayan,crs}@imsc.res.in

Abstract

We propose the following problem. For some k ≥ 1, a graph G is to be properly edge coloured such that any two adjacent vertices share at most k colours. We call this the k-intersection edge colouring. The minimum number of colours sufficient to guarantee such a colouring is the k-intersection chromatic index and is denoted χ′k(G). Let fk be defined by
fk(Δ) =
max
G : Δ(G) = Δ 
{χ′k(G)}.

We show that fk(Δ) = Θ([(Δ2)/k]). We also discuss some open problems.

Keywords: graph theory, k-intersection edge colouring, probabilistic method.

2000 Mathematics Subject Classification: 05C15, 05D40.

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Received 3 December 2007
Revised 14 February 2009
Accepted 14 February 2009