{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T07:48:04Z","timestamp":1780386484392,"version":"3.54.1"},"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>\u00a0Let $G_1,\\ldots,G_n$ be graphs on the same vertex set of size $n$, each graph with minimum degree $\\delta(G_i)\\ge n\/2$. A recent conjecture of Aharoni asserts that there exists a rainbow Hamiltonian cycle i.e. a cycle with edge set $\\{e_1,\\ldots,e_n\\}$ such that $e_i\\in E(G_i)$ for $1\\leq i \\leq n$. This can be viewed as a rainbow version of the well-known Dirac theorem. In this paper, we prove this conjecture asymptotically by showing that for every $\\varepsilon&gt;0$, there exists an integer $N&gt;0$, such that when $n&gt;N$ for any graphs $G_1,\\ldots,G_n$ on the same vertex set of size $n$ with $\\delta(G_i)\\ge (\\frac{1}{2}+\\varepsilon)n$, there exists a rainbow Hamiltonian cycle. Our main tool is the absorption technique. Additionally, we prove that with $\\delta(G_i)\\geq \\frac{n+1}{2}$ for each $i$, one can find rainbow cycles of length $3,\\ldots,n-1$.<\/jats:p>","DOI":"10.37236\/9033","type":"journal-article","created":{"date-parts":[[2021,7,16]],"date-time":"2021-07-16T11:18:00Z","timestamp":1626434280000},"source":"Crossref","is-referenced-by-count":11,"title":["Rainbow Pancyclicity in Graph Systems"],"prefix":"10.37236","volume":"28","author":[{"given":"Yangyang","family":"Cheng","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guanghui","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yi","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2021,7,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i3p24\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i3p24\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,16]],"date-time":"2021-07-16T11:18:00Z","timestamp":1626434280000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v28i3p24"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,16]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2021,7,1]]}},"URL":"https:\/\/doi.org\/10.37236\/9033","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,7,16]]},"article-number":"P3.24"}}