{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:57Z","timestamp":1753893837345,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The claw is the graph $K_{1,3}$, and the fork is the graph obtained from the claw $K_{1,3}$ by subdividing one of its edges once. In this paper, we prove a structure theorem for the class of (claw, $C_4$)-free graphs that are not quasi-line graphs, and a structure theorem for the class of (fork, $C_4$)-free graphs that uses the class of (claw, $C_4$)-free graphs as a basic class. Finally, we show that every (fork, $C_4$)-free graph $G$ satisfies $\\chi(G)\\leqslant \\lceil\\frac{3\\omega(G)}{2}\\rceil$ via these structure theorems with some additional work on coloring basic classes.<\/jats:p>","DOI":"10.37236\/9144","type":"journal-article","created":{"date-parts":[[2021,5,6]],"date-time":"2021-05-06T10:25:37Z","timestamp":1620296737000},"source":"Crossref","is-referenced-by-count":1,"title":["Square-Free Graphs with no Induced Fork"],"prefix":"10.37236","volume":"28","author":[{"given":"Maria","family":"Chudnovsky","sequence":"first","affiliation":[]},{"given":"Shenwei","family":"Huang","sequence":"additional","affiliation":[]},{"given":"T.","family":"Karthick","sequence":"additional","affiliation":[]},{"given":"Jenny","family":"Kaufmann","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2021,5,7]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i2p20\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i2p20\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,5,6]],"date-time":"2021-05-06T10:25:37Z","timestamp":1620296737000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v28i2p20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,7]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,4,9]]}},"URL":"https:\/\/doi.org\/10.37236\/9144","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2021,5,7]]},"article-number":"P2.20"}}