{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:46Z","timestamp":1753893826338,"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 graph $G$ with a perfect matching is Pfaffian if it admits an orientation $D$ such that every central cycle $C$ (i.e. $C$ is of even size and $G-V(C)$ has a perfect matching) has an odd number of edges oriented in either direction of the cycle. It is known that the number of perfect matchings of a Pfaffian graph can be computed in polynomial time. In this paper, we show that every embedding of a Pfaffian brace (i.e. 2-extendable bipartite graph)\u00a0 on a surface with a positive genus has face-width at most 3.\u00a0 Further, we study Pfaffian cubic braces and obtain a characterization of Pfaffian polyhex graphs: a polyhex graph is Pfaffian if and only if it is either non-bipartite or isomorphic to the cube, or the Heawood graph, or the Cartesian product $C_k\\times K_2$ for even integers $k\\ge 6$.<\/jats:p>","DOI":"10.37236\/3540","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:52:22Z","timestamp":1578703942000},"source":"Crossref","is-referenced-by-count":1,"title":["Face-Width of Pfaffian Braces and Polyhex Graphs on Surfaces"],"prefix":"10.37236","volume":"21","author":[{"given":"Dong","family":"Ye","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Heping","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2014,11,20]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i4p37\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i4p37\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:40:20Z","timestamp":1579257620000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v21i4p37"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,11,20]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2014,10,2]]}},"URL":"https:\/\/doi.org\/10.37236\/3540","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2014,11,20]]},"article-number":"P4.37"}}