{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T21:26:22Z","timestamp":1773696382658,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We study the rainbow version of the graph commonness property: a graph $H$ is $r$-rainbow common if the number of rainbow copies of $H$ (where all edges have distinct colors) in an $r$-coloring of edges of $K_n$ is maximized asymptotically by independently coloring each edge uniformly at random. $H$ is $r$-rainbow uncommon otherwise. We show that if $H$ has a cycle, then it is $r$-rainbow uncommon for every $r$ at least the number of edges of $H$. This generalizes a result of Erd\u0151s and Hajnal, and proves a conjecture of De Silva, Si, Tait, Tun\u00e7bilek, Yang, and Young.<\/jats:p>","DOI":"10.37236\/12594","type":"journal-article","created":{"date-parts":[[2025,7,4]],"date-time":"2025-07-04T19:54:58Z","timestamp":1751658898000},"source":"Crossref","is-referenced-by-count":1,"title":["Rainbow Common Graphs Must Be Forests"],"prefix":"10.37236","volume":"32","author":[{"given":"Yihang","family":"Sun","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2025,7,4]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i3p7\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i3p7\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,4]],"date-time":"2025-07-04T19:54:58Z","timestamp":1751658898000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v32i3p7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,4]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,7,4]]}},"URL":"https:\/\/doi.org\/10.37236\/12594","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,7,4]]},"article-number":"P3.7"}}