An upper bound for the chromatic number of line graphs

Authors:
A. D. King;B. A. Reed;A. Vetta
Affiliations:
School of Computer Science, McGill University, Canada;School of Computer Science, McGill University, Canada;School of Computer Science, McGill University, Canada
Venue:
European Journal of Combinatorics
Year:
2007

Citing 6
Cited 1

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Abstract

It was conjectured by Reed [B. Reed, @w,@a, and @g, Journal of Graph Theory 27 (1998) 177-212] that for any graph G, the graph's chromatic number @g(G) is bounded above by @?@D(G)+1+@w(G)2@?, where @D(G) and @w(G) are the maximum degree and clique number of G, respectively. In this paper we prove that this bound holds if G is the line graph of a multigraph. The proof yields a polynomial time algorithm that takes a line graph G and produces a colouring that achieves our bound.