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Determining the chromatic number of triangle-free 2P3-free graphs in polynomial time.

Broersma, H.J. and Golovach, P.A. and Paulusma, D. and Song, J. (2012) 'Determining the chromatic number of triangle-free 2P3-free graphs in polynomial time.', Theoretical computer science., 423 . pp. 1-10.


Let 2P3 denote the disjoint union of two paths on three vertices. A graph G that has no subgraph isomorphic to a graph H is called H-free. The Vertex Coloring problem is the problem to determine the chromatic number of a graph. Its computational complexity for triangle-free H-free graphs has been classified for every fixed graph H on at most 6 vertices except for the case H=2P3. This remaining case is posed as an open problem by Dabrowski, Lozin, Raman and Ries. We solve their open problem by showing polynomial-time solvability.

Item Type:Article
Keywords:Chromatic number, Triangle-free, Forbidden induced subgraph.
Full text:(AM) Accepted Manuscript
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Publisher statement:NOTICE: this is the author’s version of a work that was accepted for publication in Theoretical computer science. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Theoretical computer science, 423, 2012, 10.1016/j.tcs.2011.12.076
Date accepted:No date available
Date deposited:09 January 2015
Date of first online publication:March 2012
Date first made open access:No date available

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