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A hereditary graph class is characterized by a (possibly infinite) list of minimal forbidden induced subgraphs $$H_1,H_2,\\ldots $$<\/jats:tex-math>\n \n \n H<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:msub>\n ,<\/mml:mo>\n \n H<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n ,<\/mml:mo>\n \u2026<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>; the graphs in the class are called $$(H_1,H_2,\\ldots )$$<\/jats:tex-math>\n \n (<\/mml:mo>\n \n H<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:msub>\n ,<\/mml:mo>\n \n H<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n ,<\/mml:mo>\n \u2026<\/mml:mo>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-free. The complexity of 3-coloring is far from being understood, even for classes defined by a few small forbidden induced subgraphs. For H<\/jats:italic>-free graphs, the complexity is settled for any H<\/jats:italic> on up to seven vertices. There are only two unsolved cases on eight vertices, namely $$2P_4$$<\/jats:tex-math>\n \n 2<\/mml:mn>\n \n P<\/mml:mi>\n 4<\/mml:mn>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and $$P_8$$<\/jats:tex-math>\n \n P<\/mml:mi>\n 8<\/mml:mn>\n <\/mml:msub>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. For $$P_8$$<\/jats:tex-math>\n \n P<\/mml:mi>\n 8<\/mml:mn>\n <\/mml:msub>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-free graphs, some partial results are known, but to the best of our knowledge, $$2P_4$$<\/jats:tex-math>\n \n 2<\/mml:mn>\n \n P<\/mml:mi>\n 4<\/mml:mn>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-free graphs have not been explored yet. In this paper, we show that the 3-coloring problem is polynomial-time solvable on $$(2P_4,C_5)$$<\/jats:tex-math>\n \n (<\/mml:mo>\n 2<\/mml:mn>\n \n P<\/mml:mi>\n 4<\/mml:mn>\n <\/mml:msub>\n ,<\/mml:mo>\n \n C<\/mml:mi>\n 5<\/mml:mn>\n <\/mml:msub>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-free graphs.\n<\/jats:p>","DOI":"10.1007\/s00453-022-00937-9","type":"journal-article","created":{"date-parts":[[2022,2,15]],"date-time":"2022-02-15T06:02:42Z","timestamp":1644904962000},"page":"1526-1547","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On 3-Coloring of ($$2P_4,C_5$$)-Free Graphs"],"prefix":"10.1007","volume":"84","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4831-4079","authenticated-orcid":false,"given":"V\u00edt","family":"Jel\u00ednek","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7766-7298","authenticated-orcid":false,"given":"Tereza","family":"Klimo\u0161ov\u00e1","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8524-4036","authenticated-orcid":false,"given":"Tom\u00e1\u0161","family":"Masa\u0159\u00edk","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7955-4692","authenticated-orcid":false,"given":"Jana","family":"Novotn\u00e1","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7104-8664","authenticated-orcid":false,"given":"Aneta","family":"Pokorn\u00e1","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,2,15]]},"reference":[{"key":"937_CR1","doi-asserted-by":"publisher","unstructured":"Jel\u00ednek, V., Klimo\u0161ov\u00e1, T., Masa\u0159\u00edk, T., Novotn\u00e1, J., Pokorn\u00e1, A.: On 3-coloring of $$(2{P}_4,{C}_5)$$-free graphs. 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