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On the quantum chromatic number of a graph

Cameron, PJ; Montanaro, A; Newman, MW; Severini, S; Winter, A; (2007) On the quantum chromatic number of a graph. ELECTRON J COMB , 14 (1) , Article R81. Gold open access

Abstract

We investigate the notion of quantum chromatic number of a graph, which is the minimal number of colours necessary in a protocol in which two separated provers can convince a referee that they have a colouring of the graph. After discussing this notion from first principles, we go onto establish relations with the clique number and orthogonal representations of the graph. We also prove several general facts about this graph parameter and find large separations between the clique number and the quantum chromatic number by looking at random graphs. Finally, we show that there can be no separation between classical and quantum chromatic number if the latter is 2, nor if it is 3 in a restricted quantum model; on the other hand, we exhibit a graph on 18 vertices and 44 edges with chromatic number 5 and quantum chromatic number 4.

Type:Article
Title:On the quantum chromatic number of a graph
Open access status:An open access publication
Publisher version:http://www.combinatorics.org/
UCL classification:UCL > School of BEAMS > Faculty of Engineering Science > Computer Science

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