{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,22]],"date-time":"2026-07-22T17:45:19Z","timestamp":1784742319068,"version":"3.55.0"},"reference-count":12,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2013,8,8]],"date-time":"2013-08-08T00:00:00Z","timestamp":1375920000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2013,9]]},"abstract":"<jats:p>Given a (multi)digraph <jats:italic>H<\/jats:italic>, a digraph <jats:italic>D<\/jats:italic> is <jats:italic>H<\/jats:italic>-<jats:italic>linked<\/jats:italic> if every injective function \u03b9:<jats:italic>V(H)<\/jats:italic> \u2192 <jats:italic>V(D)<\/jats:italic> can be extended to an <jats:italic>H<\/jats:italic>-subdivision. In this paper, we give sharp degree conditions that ensure a sufficiently large digraph <jats:italic>D<\/jats:italic> is <jats:italic>H<\/jats:italic>-linked for arbitrary <jats:italic>H<\/jats:italic>. The notion of an <jats:italic>H<\/jats:italic>-linked digraph extends the classes of <jats:italic>m<\/jats:italic>-linked, <jats:italic>m<\/jats:italic>-ordered and strongly <jats:italic>m<\/jats:italic>-connected digraphs.<\/jats:p><jats:p>First, we give sharp minimum semi-degree conditions for <jats:italic>H<\/jats:italic>-linkedness, extending results of K\u00fchn and Osthus on <jats:italic>m<\/jats:italic>-linked and <jats:italic>m<\/jats:italic>-ordered digraphs. It is known that the minimum degree threshold for an undirected graph to be <jats:italic>H<\/jats:italic>-linked depends on a partition of the (undirected) graph <jats:italic>H<\/jats:italic> into three parts. Here, we show that the corresponding semi-degree threshold for <jats:italic>H<\/jats:italic>-linked digraphs depends on a partition of <jats:italic>H<\/jats:italic> into as many as nine parts.<\/jats:p><jats:p>We also determine sharp Ore\u2013Woodall-type degree-sum conditions ensuring that a digraph <jats:italic>D<\/jats:italic> is <jats:italic>H<\/jats:italic>-linked for general <jats:italic>H<\/jats:italic>. As a corollary, we obtain (previously undetermined) sharp degree-sum conditions for <jats:italic>m<\/jats:italic>-linked and <jats:italic>m<\/jats:italic>-ordered digraphs.<\/jats:p>","DOI":"10.1017\/s0963548313000278","type":"journal-article","created":{"date-parts":[[2013,8,8]],"date-time":"2013-08-08T09:27:31Z","timestamp":1375954051000},"page":"684-699","source":"Crossref","is-referenced-by-count":4,"title":["Degree Conditions for <i>H<\/i>-Linked Digraphs"],"prefix":"10.1017","volume":"22","author":[{"given":"MICHAEL","family":"FERRARA","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"MICHAEL","family":"JACOBSON","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"FLORIAN","family":"PFENDER","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2013,8,8]]},"reference":[{"key":"S0963548313000278_ref9","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548307008759"},{"key":"S0963548313000278_ref6","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548305007479"},{"key":"S0963548313000278_ref7","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0118(199909)32:1<17::AID-JGT2>3.0.CO;2-G"},{"key":"S0963548313000278_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2006.11.013"},{"key":"S0963548313000278_ref1","volume-title":"Graph Theory","author":"Diestel","year":"2005"},{"key":"S0963548313000278_ref11","doi-asserted-by":"publisher","DOI":"10.1007\/BF01275674"},{"key":"S0963548313000278_ref3","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-006-0651-6"},{"key":"S0963548313000278_ref2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.20632"},{"key":"S0963548313000278_ref5","doi-asserted-by":"publisher","DOI":"10.1137\/050624662"},{"key":"S0963548313000278_ref10","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(90)90119-K"},{"key":"S0963548313000278_ref4","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.20283"},{"key":"S0963548313000278_ref12","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-24.4.739"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548313000278","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,23]],"date-time":"2019-04-23T20:04:50Z","timestamp":1556049890000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548313000278\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,8,8]]},"references-count":12,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2013,9]]}},"alternative-id":["S0963548313000278"],"URL":"https:\/\/doi.org\/10.1017\/s0963548313000278","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,8,8]]}}}