{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:11:15Z","timestamp":1758823875864,"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>Let $D$ be a directed graph of order $n$. An anti-directed Hamilton cycle $H$ in $D$ is a Hamilton cycle in the graph underlying $D$ such that no pair of consecutive arcs in $H$ form a directed path in $D$. We prove that if $D$ is a directed graph with even order $n$ and if the indegree and the outdegree of each vertex of $D$ is at least ${2\\over 3}n$ then $D$ contains an anti-directed Hamilton cycle. This improves a bound of Grant.  Let $V(D) = P \\cup Q$ be a partition of $V(D)$.  A $(P,Q)$ vertex-oriented Hamilton cycle in $D$ is a Hamilton cycle $H$ in the graph underlying $D$ such that for each $v \\in P$, consecutive arcs of $H$ incident on $v$ do not form a directed path in $D$, and, for each $v \\in Q$, consecutive arcs of $H$ incident on $v$ form a directed path in $D$. We give sufficient conditions for the existence of a $(P,Q)$ vertex-oriented Hamilton cycle in $D$ for the cases when $|P| \\geq {2\\over 3}n$ and when ${1\\over 3}n \\leq |P| \\leq {2\\over 3}n$.  This sharpens a bound given by Badheka et al.<\/jats:p>","DOI":"10.37236\/204","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:25:10Z","timestamp":1578716710000},"source":"Crossref","is-referenced-by-count":4,"title":["Vertex-Oriented Hamilton Cycles in Directed Graphs"],"prefix":"10.37236","volume":"16","author":[{"given":"Michael J.","family":"Plantholt","sequence":"first","affiliation":[]},{"given":"Shailesh K.","family":"Tipnis","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2009,9,18]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r115\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r115\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T02:40:50Z","timestamp":1579315250000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1r115"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,9,18]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/204","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2009,9,18]]},"article-number":"R115"}}