Colouring vertices of triangle-free graphs

Lozin, Vadim; Raman, Rajiv; Ries, Bernard; Dabrowski, Konrad Kazimierz

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

Type

Communication / Conférence

Date

2010

Conference title

Graph Theoretic Concepts in Computer Science 36th International Workshop

Conference date

2010-06

Conference city

Zaros

Conference country

Grèce

Book title

Graph Theoretic Concepts in Computer Science 36th International Workshop, WG 2010, Zarós, Crete, Greece, June 28-30, 2010 Revised Papers

Book author

Thilikos, Dimitrios M.

Publisher

Springer

Series title

Lecture Notes in Computer Science

Series number

6410

Published in

Berlin

ISBN

978-3-642-16925-0

Number of pages

338

Pages

184-195

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 / Keywords

Vertex colouring; Triangle-free graphs; Polynomial-time algorithm; Clique-width