{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:12Z","timestamp":1753893852767,"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 is k-traceable if its order is at least k and each of its subdigraphs of order k is traceable. An oriented graph is a digraph without 2-cycles. The 2-traceable oriented graphs are exactly the nontrivial tournaments, so k-traceable oriented graphs may be regarded as generalized tournaments. It is well-known that all tournaments are traceable. We denote by t(k) the smallest integer bigger than or equal to k such that every k-traceable oriented graph of order at least t(k) is traceable. The Traceability Conjecture states that t(k) \u2264 2k-1 for every k \u2265 2 [van Aardt, Dunbar, Frick, Nielsen and Oellermann, A traceability conjecture for oriented graphs, Electron. J. Combin., 15(1):#R150, 2008]. We show that for k \u2265 2, every k-traceable oriented graph with independence number 2 and order at least 4k-12 is traceable. This is the last open case in giving an upper bound for t(k) that is linear in k.<\/jats:p>","DOI":"10.37236\/4727","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T22:43:11Z","timestamp":1578696191000},"source":"Crossref","is-referenced-by-count":0,"title":["A Linear Bound towards the Traceability Conjecture"],"prefix":"10.37236","volume":"22","author":[{"given":"Susan A.","family":"Van Aardt","sequence":"first","affiliation":[]},{"given":"Jean E.","family":"Dunbar","sequence":"additional","affiliation":[]},{"given":"Marietjie","family":"Frick","sequence":"additional","affiliation":[]},{"given":"Nicolas","family":"Lichiardopol","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,11,13]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i4p26\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i4p26\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:08:19Z","timestamp":1579255699000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i4p26"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,11,13]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2015,10,16]]}},"URL":"https:\/\/doi.org\/10.37236\/4727","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2015,11,13]]},"article-number":"P4.26"}}