{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T08:45:56Z","timestamp":1770972356332,"version":"3.50.1"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2019,5,16]],"date-time":"2019-05-16T00:00:00Z","timestamp":1557964800000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,5,16]],"date-time":"2019-05-16T00:00:00Z","timestamp":1557964800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,5,16]],"date-time":"2019-05-16T00:00:00Z","timestamp":1557964800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>A graph on $n$ vertices is equitably $k$-colorable if it is $k$-colorable and every color is used either $\\left\\lfloor n\/k \\right\\rfloor$ or $\\left\\lceil n\/k \\right\\rceil$ times.   Such a problem appears to be considerably harder than vertex coloring, being $\\mathsf{NP\\text{-}Complete}$ even for cographs and interval graphs.   In this work, we prove that it is $\\mathsf{W[1]\\text{-}Hard}$ for block graphs and for disjoint union of split graphs when parameterized by the number of colors; and $\\mathsf{W[1]\\text{-}Hard}$ for $K_{1,4}$-free interval graphs when parameterized by treewidth, number of colors and maximum degree, generalizing a result by Fellows et al. (2014) through a much simpler reduction.   Using a previous result due to Dominique de Werra (1985), we establish a dichotomy for the complexity of equitable coloring of chordal graphs based on the size of the largest induced star.   Finally, we show that \\textsc{equitable coloring} is $\\mathsf{FPT}$ when parameterized by the treewidth of the complement graph.<\/jats:p>","DOI":"10.23638\/dmtcs-21-1-8","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T16:55:19Z","timestamp":1743699319000},"source":"Crossref","is-referenced-by-count":1,"title":["Parameterized Complexity of Equitable Coloring"],"prefix":"10.23638","volume":"vol. 21 no. 1, ICGT 2018","author":[{"given":"Guilherme de C. M.","family":"Gomes","sequence":"first","affiliation":[]},{"given":"Carlos V. G. C.","family":"Lima","sequence":"additional","affiliation":[]},{"given":"Vin\u00edcius F. dos","family":"Santos","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2019,5,16]]},"container-title":["Discrete Mathematics &amp; Theoretical Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1810.13036v3","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1810.13036v3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T16:55:19Z","timestamp":1743699319000},"score":1,"resource":{"primary":{"URL":"http:\/\/dmtcs.episciences.org\/4948"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,16]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/dmtcs-21-1-8","relation":{"has-preprint":[{"id-type":"arxiv","id":"1810.13036v2","asserted-by":"subject"},{"id-type":"arxiv","id":"1810.13036v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1810.13036","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1810.13036","asserted-by":"subject"}]},"ISSN":["1365-8050"],"issn-type":[{"value":"1365-8050","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,5,16]]},"article-number":"4948"}}