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In this paper we study the chromatic number for graphs with forbidden induced subgraphs. We focus our interest on graph classes (defined in terms of forbidden induced subgraphs) for which the question of 3-colourability can be decided in polynomial time and, if so, a proper 3-colouring can be determined also in polynomial time. Note that the 3-colourability decision problem is a well-known NP-complete...
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