{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,20]],"date-time":"2024-06-20T15:18:23Z","timestamp":1718896703562},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"This is a continuation of our paper \"A Theory of Pfaffian Orientations I: Perfect Matchings and Permanents\". We present a new combinatorial way to compute the generating functions of $T$-joins and $k$-cuts of graphs. As a consequence, we show that the computational problem to find the maximum weight of an edge-cut is polynomially solvable for the instances $(G,w)$ where $G$ is a graph embedded on an arbitrary fixed orientable surface and the weight function $w$ has only a bounded number of different values. We also survey the related results concerning a duality of the Tutte polynomial, and present an application for the weight enumerator of a binary code. In a continuation of this paper which is in preparation we present an application to the Ising problem of three-dimensional crystal structures.<\/jats:p>","DOI":"10.37236\/1439","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:01:58Z","timestamp":1578708118000},"source":"Crossref","is-referenced-by-count":17,"title":["On the Theory of Pfaffian Orientations. II. $T$-joins, $k$-cuts, and Duality of Enumeration"],"prefix":"10.37236","volume":"6","author":[{"given":"Anna","family":"Galluccio","sequence":"first","affiliation":[]},{"given":"Martin","family":"Loebl","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[1998,5,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v6i1r7\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v6i1r7\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T06:09:20Z","timestamp":1579327760000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v6i1r7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,5,22]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[1999,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1439","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,5,22]]}}}