On 3-Coloring of ( $$2P_4,C_5$$ 2 P 4 , C 5 )-Free Graphs
Algorithmica(2022)
摘要
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
$$H_1,H_2,\ldots $$
; the graphs in the class are called
$$(H_1,H_2,\ldots )$$
-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
$$2P_4$$
and
$$P_8$$
. For
$$P_8$$
-free graphs, some partial results are known, but to the best of our knowledge,
$$2P_4$$
-free graphs have not been explored yet. In this paper, we show that the 3-coloring problem is polynomial-time solvable on
$$(2P_4,C_5)$$
-free graphs.
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关键词
3-Coloring,Hereditary classes,-Free graphs,Cographs,05C75
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