{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:19:53Z","timestamp":1759637993159,"version":"3.41.2"},"reference-count":9,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12071265"],"award-info":[{"award-number":["12071265"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province","doi-asserted-by":"publisher","award":["ZR2019MA032"],"award-info":[{"award-number":["ZR2019MA032"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2023,4]]},"abstract":"<jats:p> For a graph G, [Formula: see text], [Formula: see text] represent the clique number and the chromatic number of G, respectively. A hereditary family [Formula: see text] of graphs is called [Formula: see text]-bounded with [Formula: see text]-binding function [Formula: see text] if [Formula: see text] for all [Formula: see text]. A result of Schiermeyer shows that the class of [Formula: see text]-free graphs has a [Formula: see text]-binding function [Formula: see text] [L. Esperet, L. Lemoine, F. Maffray and G. Morel, The chromatic number of [Formula: see text]-free graphs, Discrete Math.\u00a0313 (2013) 743\u2013754]. In this paper, we prove that the class of [Formula: see text]-free graphs has a [Formula: see text]-binding function [Formula: see text]. For the class of [Formula: see text]-free graphs, we give a [Formula: see text]-binding function [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s1793830922500902","type":"journal-article","created":{"date-parts":[[2022,4,18]],"date-time":"2022-04-18T09:20:59Z","timestamp":1650273659000},"source":"Crossref","is-referenced-by-count":2,"title":["On the chromatic number of (P5,dart)-free graphs"],"prefix":"10.1142","volume":"15","author":[{"given":"Weilun","family":"Xu","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Shandong Normal University, Jinan, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6323-2923","authenticated-orcid":false,"given":"Xia","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Shandong Normal University, Jinan, P. R. 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Analysis and Applications (Pokrzywna,1985)","volume":"19","author":"Gy\u00e1rf\u00e1s A.","year":"1987"},{"key":"S1793830922500902BIB006","doi-asserted-by":"crossref","first-page":"1447","DOI":"10.1007\/s00373-015-1651-1","volume":"32","author":"Karthick T.","year":"2016","journal-title":"Graphs Comb."},{"issue":"7","key":"S1793830922500902BIB007","doi-asserted-by":"crossref","first-page":"1940","DOI":"10.1016\/j.disc.2015.11.020","volume":"339","author":"Schiermeyer I.","year":"2016","journal-title":"Discrete Math."},{"key":"S1793830922500902BIB008","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00373-018-1999-0","volume":"35","author":"Schiermeyer I.","year":"2019","journal-title":"Graphs Comb."},{"key":"S1793830922500902BIB009","first-page":"557","volume-title":"The Theory and Applications of Graphs","author":"Sumner D.","year":"1981"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830922500902","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,24]],"date-time":"2023-03-24T10:14:43Z","timestamp":1679652883000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S1793830922500902"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,18]]},"references-count":9,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2023,4]]}},"alternative-id":["10.1142\/S1793830922500902"],"URL":"https:\/\/doi.org\/10.1142\/s1793830922500902","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2022,4,18]]},"article-number":"2250090"}}