{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,23]],"date-time":"2025-03-23T04:21:29Z","timestamp":1742703689105,"version":"3.40.2"},"reference-count":0,"publisher":"Combinatorial Press","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ars Comb."],"published-print":{"date-parts":[[2025,3,30]]},"abstract":"<jats:p>A proper total coloring of a graph \\( G \\) such that there are at least 4 colors on those vertices and edges incident with a cycle of \\( G \\), is called an acyclic total coloring. The acyclic total chromatic number of \\( G \\), denoted by \\( \\chi^{''}_{a}(G) \\), is the smallest number of colors such that \\( G \\) has an acyclic total coloring. In this article, we prove that for any graph \\( G \\) with \\( \\Delta(G)=\\Delta \\) which satisfies \\( \\chi^{''}(G)\\leq A \\) for some constant \\( A \\), and for any integer \\( r \\), \\( 1\\leq r \\leq 2\\Delta \\), there exists a constant \\( c&gt;0 \\) such that if \\( g(G)\\geq\\frac{c\\Delta}{r}\\log\\frac{\\Delta^{2}}{r} \\), then \\( \\chi^{''}_{a}(G)\\leq A+r \\).<\/jats:p>","DOI":"10.61091\/ars162-01","type":"journal-article","created":{"date-parts":[[2025,3,22]],"date-time":"2025-03-22T16:54:46Z","timestamp":1742662486000},"page":"3-12","source":"Crossref","is-referenced-by-count":0,"title":["Acyclic total coloring of graphs with large girths"],"prefix":"10.61091","volume":"162","author":[{"name":"School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, P. R. China","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoya","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenyao","family":"Song","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"name":"School of Mathematics and Statistics, Zaozhuang University, Zaozhuang, 277160, P. R. China","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lianying","family":"Miao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"name":"School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, P. R. China","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"39747","published-online":{"date-parts":[[2025,3,30]]},"container-title":["Ars Combinatoria"],"original-title":[],"deposited":{"date-parts":[[2025,3,22]],"date-time":"2025-03-22T16:54:48Z","timestamp":1742662488000},"score":1,"resource":{"primary":{"URL":"https:\/\/combinatorialpress.com\/ars-articles\/volume-162\/acyclic-total-coloring-of-graphs-with-large-girths\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,30]]},"references-count":0,"URL":"https:\/\/doi.org\/10.61091\/ars162-01","relation":{},"ISSN":["0381-7032","2817-5204"],"issn-type":[{"value":"0381-7032","type":"print"},{"value":"2817-5204","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,30]]}}}