{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,24]],"date-time":"2025-10-24T08:20:52Z","timestamp":1761294052636,"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>A Gray code is a Hamilton path $H$ on the $n$-cube, $Q_n$.   By labeling each edge of $Q_n$ with the dimension that changes between its incident vertices, a Gray code can be thought of as a sequence $H = t_1,t_2,\\ldots,t_{N-1}$  (with $N = 2^n$ and each $t_i$ satisfying $1 \\le t_i \\le n$). The sequence $H$ defines an (undirected) graph of transitions, $G_H$, whose vertex set is $\\{1,2,\\ldots,n\\}$ and whose edge set $E(G_H) = \\{ [t_i,t_{i+1}] \\mid 1 \\le i \\le N-1 \\}$. A $G$-code is a Hamilton path $H$ whose graph of transitions is a subgraph of $G$; if $H$ is a Hamilton cycle then it is a  cyclic $G$-code. The classic binary reflected Gray code is a cyclic $K_{1,n}$-code. We prove that every tree $T$ of diameter 4 has a $T$-code, and that no tree $T$ of diameter 3 has a $T$-code. <\/jats:p>","DOI":"10.37236\/1235","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:26:48Z","timestamp":1578706008000},"source":"Crossref","is-referenced-by-count":10,"title":["Transition Restricted Gray Codes"],"prefix":"10.37236","volume":"3","author":[{"given":"Bette","family":"Bultena","sequence":"first","affiliation":[]},{"given":"Frank","family":"Ruskey","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[1996,3,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v3i1r11\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v3i1r11\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T06:17:41Z","timestamp":1579328261000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v3i1r11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,3,14]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[1996,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1235","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[1996,3,14]]},"article-number":"R11"}}