Abstract
The vertex 3-colourability problem is to decide whether the vertex set of a given graph can be split into three subsets of pairwise non-adjacent vertices. This problem is known to be NP-complete in a certain class of graphs, defined by an explicit description of allowed 5-vertex induced subgraphs in them. In the present paper, we improve this result by showing that the vertex 3-colourability problem remains NP-complete for a reduced set of allowed 5-vertex induced structures. It gives a step towards obtaining a complete complexity dichotomy for the mentioned problem and all the classes, defined by 5-vertex forbidden induced prohibitions.
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The article was prepared within the framework of the Basic Research Program at the National Research University Higher School of Economics (HSE).
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Malyshev, D.S., Pristavchenko, O.V. An intractability result for the vertex 3-colourability problem. Optim Lett 16, 1403–1409 (2022). https://doi.org/10.1007/s11590-022-01859-9
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DOI: https://doi.org/10.1007/s11590-022-01859-9