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Colouring vertices of triangle-free graphs without forests

Dabrowski, Konrad K. ; Lozin, Vadim ; Raman, Rajiv ; Ries, Bernard

In: Discrete Mathematics, 2012, vol. 312, no. 7, p. 1372-1385

The vertex colouring problem is known to be NP-complete in the class of triangle-free graphs. Moreover, it is NP-complete in any subclass of triangle-free graphs defined by a finite collection of forbidden induced subgraphs, each of which contains a cycle. In this paper, we study the vertex colouring problem in subclasses of triangle-free graphs obtained by forbidding graphs without cycles, i.e.,...