2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Stefan Felsner (ed.)
DMTCS Conference Volume AE (2005), pp. 151156
author:  Andrew D. King, Bruce A. Reed and Adrian R. Vetta 

title:  An upper bound for the chromatic number of line graphs 
keywords:  
abstract: 
It was conjectured by Reed [reed98conjecture] that for any
graph
G
, the graph's chromatic number
χ(G)
is bounded above by
⌈Δ(G) +1 + ω(G) / 2⌉
, where
Δ(G)
and
ω(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.

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reference:  Andrew D. King and Bruce A. Reed and Adrian R. Vetta (2005), An upper bound for the chromatic number of line graphs, in 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), Stefan Felsner (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AE, pp. 151156 
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