{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:12Z","timestamp":1753893792551,"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 1997, Ng and Schultz introduced the idea of cycle orderability. For a positive integer $k$,  a graph $G$ is k-ordered if for every ordered sequence of $k$ vertices, there is a cycle that encounters the vertices of the sequence in the given order.  If the cycle is also a hamiltonian cycle, then $G$ is said to be k-ordered hamiltonian. We give minimum degree conditions and sum of degree conditions for nonadjacent vertices that imply a balanced bipartite graph to be $k$-ordered hamiltonian. For example, let $G$ be a balanced  bipartite graph on $2n$ vertices, $n$ sufficiently large.  We show that for any positive integer $k$,  if the minimum degree of $G$ is at least $(2n+k-1)\/4$, then $G$ is $k$-ordered hamiltonian.<\/jats:p>","DOI":"10.37236\/1704","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:29:38Z","timestamp":1578709778000},"source":"Crossref","is-referenced-by-count":9,"title":["On $k$-Ordered Bipartite Graphs"],"prefix":"10.37236","volume":"10","author":[{"given":"Jill R.","family":"Faudree","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ronald J.","family":"Gould","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Florian","family":"Pfender","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Allison","family":"Wolf","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2003,4,15]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v10i1r11\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v10i1r11\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:09:37Z","timestamp":1579324177000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v10i1r11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,4,15]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2003,1,6]]}},"URL":"https:\/\/doi.org\/10.37236\/1704","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2003,4,15]]},"article-number":"R11"}}