(Star, k)-colourings of graphs with bounded treewidth


We study a generalization of graph colouring define as follows. Given a graph G, a (star, k)-colouring of G is a colouring c : V(G) → {1, ..., k} such that every colour class induces a star. We propose an O*(2^(O(tw))k^(tw)-time algorithm that decides whether a graph G of treewidth at most tw admits a (star, k)-colouring. This resolves an open problem posed by Angelini et al. in 2017. Our approach can be extended to other defective colouring models.

Palavras-chave: defective colouring, star colouring, parameterized algorithms


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WEFFORT-SANTOS, C. A.; PEDROSA, L. L. C.. (Star, k)-colourings of graphs with bounded treewidth. In: ENCONTRO DE TEORIA DA COMPUTAÇÃO (ETC), 5. , 2020, Cuiabá. Anais [...]. Porto Alegre: Sociedade Brasileira de Computação, 2020 . p. 41-44. ISSN 2595-6116. DOI: https://doi.org/10.5753/etc.2020.11085.