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On 3-Coloring of ([Formula: see text] )-Free Graphs

The 3-coloring of hereditary graph classes has been a deeply-researched problem in the last decade. A hereditary graph class is characterized by a (possibly infinite) list of minimal forbidden induced subgraphs [Formula: see text] ; the graphs in the class are called [Formula: see text] -free. The c...

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Detalles Bibliográficos
Autores principales: Jelínek, Vít, Klimošová, Tereza, Masařík, Tomáš, Novotná, Jana, Pokorná, Aneta
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9148298/
https://www.ncbi.nlm.nih.gov/pubmed/35651539
http://dx.doi.org/10.1007/s00453-022-00937-9
Descripción
Sumario:The 3-coloring of hereditary graph classes has been a deeply-researched problem in the last decade. A hereditary graph class is characterized by a (possibly infinite) list of minimal forbidden induced subgraphs [Formula: see text] ; the graphs in the class are called [Formula: see text] -free. The complexity of 3-coloring is far from being understood, even for classes defined by a few small forbidden induced subgraphs. For H-free graphs, the complexity is settled for any H on up to seven vertices. There are only two unsolved cases on eight vertices, namely [Formula: see text] and [Formula: see text] . For [Formula: see text] -free graphs, some partial results are known, but to the best of our knowledge, [Formula: see text] -free graphs have not been explored yet. In this paper, we show that the 3-coloring problem is polynomial-time solvable on [Formula: see text] -free graphs.