ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory


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


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

The Institute of Mathematical Sciences
Taramani, Chennai-600113, India
e-mail: {rahulm,narayan,crs}


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) =
G : Δ(G) = Δ 

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