{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:43:46Z","timestamp":1759063426218,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>In 1975, P. Erd\u0151s proposed the problem of determining the maximum number $f(n)$ of edges in a simple graph of $n$ vertices in which any two cycles are of different lengths. In this paper, it is proved that $$f(n)\\geq n+32t-1$$ for $t=27720r+169 \\,\\ (r\\geq 1)$ and $n\\geq {{6911}\\over {16}}t^{2}+{{514441}\\over {8}}t-{{3309665}\\over {16}}$. Consequently, $\\liminf _{n \\to \\infty} {f(n)-n \\over \\sqrt n} \\geq \\sqrt {2 + {2562 \\over 6911}}.$<\/jats:p>","DOI":"10.37236\/1594","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:06:49Z","timestamp":1578690409000},"source":"Crossref","is-referenced-by-count":4,"title":["A Lower Bound for the Number of Edges in a Graph Containing No Two Cycles of the Same Length"],"prefix":"10.37236","volume":"8","author":[{"given":"Chunhui","family":"Lai","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2001,10,20]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i1n9\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i1n9\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T00:16:36Z","timestamp":1579306596000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v8i1n9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,10,20]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2001,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1594","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2001,10,20]]},"article-number":"N9"}}