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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...
Autores principales: | , , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer US
2022
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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 |
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. |
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