{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T09:54:02Z","timestamp":1773222842738,"version":"3.50.1"},"reference-count":21,"publisher":"Elsevier BV","issue":"1-2","license":[{"start":{"date-parts":[[1989,10,1]],"date-time":"1989-10-01T00:00:00Z","timestamp":623203200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[1989,10,1]],"date-time":"1989-10-01T00:00:00Z","timestamp":623203200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2003,4,15]],"date-time":"2003-04-15T00:00:00Z","timestamp":1050364800000},"content-version":"vor","delay-in-days":4944,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Discrete Applied Mathematics"],"published-print":{"date-parts":[[1989,10]]},"DOI":"10.1016\/0166-218x(89)90053-x","type":"journal-article","created":{"date-parts":[[2002,7,25]],"date-time":"2002-07-25T23:43:01Z","timestamp":1027640581000},"page":"179-190","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":61,"title":["Pfaffian orientations, 0\u20131 permanents, and even cycles in directed graphs"],"prefix":"10.1016","volume":"25","author":[{"given":"Vijay V.","family":"Vazirani","sequence":"first","affiliation":[]},{"given":"Milhalis","family":"Yannakakis","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/0166-218X(89)90053-X_BIB1","series-title":"Graphs and Hypergraphs","author":"Berge","year":"1973"},{"key":"10.1016\/0166-218X(89)90053-X_BIB2","unstructured":"R.A. Brualdi, Counting permutations with restricted positions: Permanents of (0, 1)-matrices, Linear Algebra Appl., to appear."},{"key":"10.1016\/0166-218X(89)90053-X_BIB3","unstructured":"S. Friedland, Every 7-regular digraph contains an even cycle, to appear."},{"issue":"1","key":"10.1016\/0166-218X(89)90053-X_BIB4","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1007\/BF02579407","article-title":"Constructing a maximum matching is in random NC","volume":"6","author":"Karp","year":"1986","journal-title":"Combinatorica"},{"key":"10.1016\/0166-218X(89)90053-X_BIB5","series-title":"Graph Theory and Theoretical Physics","first-page":"43","article-title":"Graph theory and crystal physics","author":"Kasteleyn","year":"1967"},{"key":"10.1016\/0166-218X(89)90053-X_BIB6","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/0024-3795(84)90164-2","article-title":"Sign solvability revisited","volume":"59","author":"Klee","year":"1984","journal-title":"Linear Algebra Appl."},{"key":"10.1016\/0166-218X(89)90053-X_BIB7","first-page":"47","article-title":"Even circuits in directed graphs and Lov\u00e1sz's conjecture","volume":"7","author":"Koh","year":"1976","journal-title":"Bull. Malaysian Math. Soc."},{"key":"10.1016\/0166-218X(89)90053-X_BIB8","first-page":"63","article-title":"An extension of Kasteleyn's method of enumerating the 1-factors of planar graphs","volume":"403","author":"Little","year":"1974"},{"key":"10.1016\/0166-218X(89)90053-X_BIB9","series-title":"Recent Advances in Graph Theory","article-title":"Problem 2","author":"Lov\u00e1sz","year":"1975"},{"key":"10.1016\/0166-218X(89)90053-X_BIB10","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/0095-8956(87)90021-9","article-title":"Matching structure and the matching lattice","volume":"43","author":"Lov\u00e1sz","year":"1987","journal-title":"J. Combin. Theory Ser. B"},{"key":"10.1016\/0166-218X(89)90053-X_BIB11","series-title":"Matching Theory","author":"Lov\u00e1sz","year":"1986"},{"key":"10.1016\/0166-218X(89)90053-X_BIB12","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1002\/jgt.3190100203","article-title":"On digraphs with the odd cycle property","volume":"10","author":"Manber","year":"1986","journal-title":"J. Graph Theory"},{"key":"10.1016\/0166-218X(89)90053-X_BIB13","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1215\/ijm\/1255630882","article-title":"On the relation between the determinant and the permanent","volume":"5","author":"Marcus","year":"1961","journal-title":"Illinois J. Math."},{"issue":"1","key":"10.1016\/0166-218X(89)90053-X_BIB14","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1007\/BF02579206","article-title":"Matching is as easy as matrix multiplication","volume":"7","author":"Mulmuley","year":"1987","journal-title":"Combinatorica"},{"issue":"3","key":"10.1016\/0166-218X(89)90053-X_BIB15","first-page":"271","article-title":"Aufgabe 424","volume":"20","author":"Polya","year":"1913","journal-title":"Arch. Math. Phys."},{"key":"10.1016\/0166-218X(89)90053-X_BIB16","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/0095-8956(87)90061-X","article-title":"Characterization of even directed graphs","volume":"42","author":"Seymour","year":"1987","journal-title":"J. Combin. Theory Ser. B"},{"key":"10.1016\/0166-218X(89)90053-X_BIB17","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/S0195-6698(85)80025-1","article-title":"Even cycles in directed graphs","volume":"6","author":"Thomassen","year":"1985","journal-title":"European J. Combin."},{"key":"10.1016\/0166-218X(89)90053-X_BIB18","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/0024-3795(86)90179-5","article-title":"Sign-nonsingular matrices and even cycles in directed graphs","volume":"75","author":"Thomassen","year":"1986","journal-title":"Linear Algebra Appl."},{"key":"10.1016\/0166-218X(89)90053-X_BIB19","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/0304-3975(79)90044-6","article-title":"The complexity of computing the permanent","volume":"8","author":"Valiant","year":"1979","journal-title":"Theoret. Comput. Sci."},{"key":"10.1016\/0166-218X(89)90053-X_BIB20","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/0304-3975(86)90135-0","article-title":"NP is as easy as detecting unique solutions","volume":"47","author":"Valiant","year":"1986","journal-title":"Theoret. Comput. Sci."},{"issue":"2","key":"10.1016\/0166-218X(89)90053-X_BIB21","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1016\/0890-5401(89)90017-5","article-title":"NC algorithms for computing the number of perfect matchings in K3, 3-free graphs and related problems","volume":"80","author":"Vazirani","year":"1989","journal-title":"Inform. and Computation"}],"container-title":["Discrete Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:0166218X8990053X?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:0166218X8990053X?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,9,9]],"date-time":"2025-09-09T20:52:56Z","timestamp":1757451176000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/0166218X8990053X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1989,10]]},"references-count":21,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[1989,10]]}},"alternative-id":["0166218X8990053X"],"URL":"https:\/\/doi.org\/10.1016\/0166-218x(89)90053-x","relation":{},"ISSN":["0166-218X"],"issn-type":[{"value":"0166-218X","type":"print"}],"subject":[],"published":{"date-parts":[[1989,10]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Pfaffian orientations, 0\u20131 permanents, and even cycles in directed graphs","name":"articletitle","label":"Article Title"},{"value":"Discrete Applied Mathematics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/0166-218X(89)90053-X","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"converted-article","name":"content_type","label":"Content Type"},{"value":"Copyright \u00a9 1989 Published by Elsevier B.V.","name":"copyright","label":"Copyright"}]}}