Colouring vertices of triangle-free graphs
Lozin, Vadim; Raman, Rajiv; Ries, Bernard; Dabrowski, Konrad Kazimierz (2010), Colouring vertices of triangle-free graphs, in Thilikos, Dimitrios M., Graph Theoretic Concepts in Computer Science 36th International Workshop, WG 2010, Zarós, Crete, Greece, June 28-30, 2010 Revised Papers, Springer : Berlin, p. 184-195. http://dx.doi.org/10.1007/978-3-642-16926-7_18
TypeCommunication / Conférence
Conference titleGraph Theoretic Concepts in Computer Science 36th International Workshop
Book titleGraph Theoretic Concepts in Computer Science 36th International Workshop, WG 2010, Zarós, Crete, Greece, June 28-30, 2010 Revised Papers
Book authorThilikos, Dimitrios M.
Series titleLecture Notes in Computer Science
Number of pages338
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Abstract (EN)The vertex colouring problem is known to be NP-comple-te in the class of triangle-free graphs. Moreover, it remains NP-complete even if we additionally exclude a graph F which is not a forest. We study the computational complexity of the problem in (K3,F)-free graphs with F being a forest. From known results it follows that for any forest F on 5 vertices the vertex colouring problem is polynomial-time solvable in the class of (K3,F)-free graphs. In the present paper, we show that the problem is also polynomial-time solvable in many classes of (K3,F)-free graphs with F being a forest on 6 vertices.
Subjects / KeywordsVertex colouring; Triangle-free graphs; Polynomial-time algorithm; Clique-width
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