{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T11:32:05Z","timestamp":1777548725904,"version":"3.51.4"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>\u00a0In the homomorphism order of digraphs, a duality pair is an ordered pair of digraphs $(G,H)$ such that for any digraph, $D$, $G\\to D$ if and only if $D\\not \\to H$. The directed path on $k+1$ vertices together with the transitive tournament on $k$ vertices is a classic example of a duality pair.\r\nIn this work, for every undirected cycle $C$ we find an orientation $C_D$ and an oriented path $P_C$, such that $(P_C,C_D)$ is a duality pair. As a consequence we obtain that there is a finite set, $F_C$, such that an undirected graph is homomorphic to $C$, if and only if it admits an $F_C$-free orientation. As a byproduct of the proposed duality pairs, we show that if $T$ is an oriented tree of height at most $3$, one can choose a dual of $T$ of linear size with respect to the size of $T$.<\/jats:p>","DOI":"10.37236\/9747","type":"journal-article","created":{"date-parts":[[2021,7,16]],"date-time":"2021-07-16T11:17:55Z","timestamp":1626434275000},"source":"Crossref","is-referenced-by-count":1,"title":["Duality Pairs and Homomorphisms to Oriented and Unoriented Cycles"],"prefix":"10.37236","volume":"28","author":[{"given":"Santiago","family":"Guzm\u00e1n-Pro","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"C\u00e9sar","family":"Hern\u00e1ndez-Cruz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2021,7,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i3p17\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i3p17\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,16]],"date-time":"2021-07-16T11:17:55Z","timestamp":1626434275000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v28i3p17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,16]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2021,7,1]]}},"URL":"https:\/\/doi.org\/10.37236\/9747","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,7,16]]},"article-number":"P3.17"}}