{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:00Z","timestamp":1753893840907,"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>The nodes of the de Bruijn graph $B(d,3)$ consist of all strings of length $3$, taken from an alphabet of size $d$, with edges between words which are distinct substrings of a word of length $4$.  We give an inductive characterization of the maximum independent sets of the de Bruijn graphs $B(d,3)$ and for the de Bruijn graph of diameter three with loops removed, for arbitrary alphabet size.  We derive a recurrence relation and an exponential generating function for their number. This recurrence allows us to construct exponentially many comma-free codes of length 3 with maximal cardinality.<\/jats:p>","DOI":"10.37236\/681","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:41:25Z","timestamp":1578714085000},"source":"Crossref","is-referenced-by-count":1,"title":["The Maximum Independent Sets of de Bruijn Graphs of Diameter  3"],"prefix":"10.37236","volume":"18","author":[{"given":"Dustin A.","family":"Cartwright","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mar\u00eda Ang\u00e9lica","family":"Cueto","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Enrique A.","family":"Tobis","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,10,3]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p194\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p194\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:01:21Z","timestamp":1579302081000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p194"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,10,3]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/681","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,10,3]]},"article-number":"P194"}}