Coloring vertices of claw-free graphs in three colors

Vadim Lozin () and Christopher Purcell ()
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Vadim Lozin: The University of Warwick
Christopher Purcell: The University of Warwick

Journal of Combinatorial Optimization, 2014, vol. 28, issue 2, No 9, 462-479

Abstract: Abstract We study the computational complexity of the vertex 3-colorability problem in the class of claw-free graphs. Both the problem and the class received much attention in the literature, separately of each other. However, very little is known about the 3-colorability problem restricted to the class of claw-free graphs beyond the fact the problem is NP-complete under this restriction. In this paper we first strengthen this negative fact by revealing various further restrictions under which the problem remains NP-complete. Then we derive a number of positive results that deal with polynomially solvable cases of the problem in the class of claw-free graphs.

Keywords: Vertex 3-colorability; Claw-free graphs; NP-completeness; Polynomial-time algorithm (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10878-012-9577-5

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