{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:29Z","timestamp":1753893809480,"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 $G$ be a graph. A Hamilton path in $G$ is a path containing every vertex of $G$. The graph $G$ is traceable if it contains a Hamilton path, while $G$ is $k$-traceable if every induced subgraph of $G$ of order $k$ is traceable. In this paper, we study hamiltonicity of $k$-traceable graphs. For $k \\geq 2$ an integer, we define $H(k)$ to be the largest integer such that there exists a $k$-traceable graph of order $H(k)$ that is nonhamiltonian. For $k \\le 10$, we determine the exact value of $H(k)$. For $k \\ge 11$, we show that $k+2 \\le H(k) \\le \\frac{1}{2}(3k-5)$.<\/jats:p>","DOI":"10.37236\/550","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T22:52:18Z","timestamp":1578696738000},"source":"Crossref","is-referenced-by-count":0,"title":["Hamiltonicity of $k$-Traceable Graphs"],"prefix":"10.37236","volume":"18","author":[{"given":"Frank","family":"Bullock","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peter","family":"Dankelmann","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marietjie","family":"Frick","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael A.","family":"Henning","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ortrud R.","family":"Oellermann","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Susan","family":"Van Aardt","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,3,24]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p63\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p63\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T18:15:12Z","timestamp":1579284912000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p63"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,3,24]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/550","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,3,24]]},"article-number":"P63"}}