{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,18]],"date-time":"2025-12-18T14:11:17Z","timestamp":1766067077554,"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 this paper we study the length of the longest induced cycle in the unit circulant graph $X_n = Cay({\\Bbb Z}_n; {\\Bbb Z}_n^*)$, where ${\\Bbb Z}_n^*$ is the group of units in ${\\Bbb Z}_n$.  Using residues modulo the primes dividing $n$, we introduce a representation of the vertices that reduces the problem to a purely combinatorial question of comparing strings of symbols.  This representation allows us to prove that the multiplicity of each prime dividing $n$, and even the value of each prime (if sufficiently large) has no effect on the length of the longest induced cycle in $X_n$.  We also see that if $n$ has $r$ distinct prime divisors, $X_n$ always contains an induced cycle of length $2^r+2$, improving the $r \\ln r$ lower bound of Berrezbeitia and Giudici.  Moreover, we extend our results for $X_n$ to conjunctions of complete $k_i$-partite graphs, where $k_i$ need not be finite, and also to unit circulant graphs on any quotient of a Dedekind domain.<\/jats:p>","DOI":"10.37236\/1949","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:09:20Z","timestamp":1578719360000},"source":"Crossref","is-referenced-by-count":26,"title":["Longest Induced Cycles in Circulant Graphs"],"prefix":"10.37236","volume":"12","author":[{"given":"Elena D.","family":"Fuchs","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2005,10,13]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r52\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r52\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:40:37Z","timestamp":1579322437000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v12i1r52"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,10,13]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2005,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1949","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2005,10,13]]},"article-number":"R52"}}