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- W2077936668 abstract "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., forests, and prove polynomial-time solvability of the problem in many classes of this type. In particular, our paper, combined with some previously known results, provides a complete description of the complexity status of the problem in subclasses of triangle-free graphs obtained by forbidding a forest with at most 6 vertices." @default.
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- W2077936668 date "2012-04-01" @default.
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- W2077936668 title "Colouring vertices of triangle-free graphs without forests" @default.
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- W2077936668 doi "https://doi.org/10.1016/j.disc.2011.12.012" @default.
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