{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:54Z","timestamp":1753893834086,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A digraph $D$ is traceable if it contains a path visiting every vertex, and hypotraceable if $D$ is not traceable, but $D-v$ is traceable for every vertex $v\\in V(D)$. Van Aardt, Frick, Katreni\u010d\u00a0and Nielsen [Discrete Math. 11(2011), 1273-1280] showed that there exists a hypotraceable oriented graph of order $n$ for every $n\\geq 8$, except possibly for $n=9$ or $11$. These two outstanding existence questions for hypotraceable oriented graphs are settled in this paper --- the first in the negative and the second in the affirmative.\u00a0 Furthermore, $D$ is $k$-traceable if $D$ has at least $k$ vertices and each of its induced subdigraphs of order $k$ is traceable.\u00a0 It is known that for $k\\leq 6$ every k-traceable oriented graph is traceable and that for $k=7$ and each $k\\geq 9$ there exist nontraceable $k$-traceable oriented graphs of order $k+1$. The Traceability Conjecture states that for $k\\geq 2$ every $k$-traceable oriented graph of order $n\\geq 2k-1$ is traceable. In this paper it is shown via computer searches that all $7$-traceable and $8$-traceable oriented graphs of orders $9$, $10$ and $11$ are traceable, and that all $9$-traceable oriented graphs of order $11$ are traceable. All hypotraceable graphs of order $10$ are also found. Recently, these results are used to prove that the Traceability Conjecture also holds for $k =7, 8$ and 9, except possibly when $k=9$ and $22\\leq n\\leq 32$.<\/jats:p>","DOI":"10.37236\/2499","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:12:32Z","timestamp":1578705152000},"source":"Crossref","is-referenced-by-count":1,"title":["Computational Results on the Traceability of Oriented Graphs of Small Order"],"prefix":"10.37236","volume":"20","author":[{"given":"Alewyn","family":"Burger","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,11,29]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i4p23\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i4p23\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:10:51Z","timestamp":1579259451000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i4p23"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,11,29]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2013,10,14]]}},"URL":"https:\/\/doi.org\/10.37236\/2499","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,11,29]]},"article-number":"P23"}}