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A Polynomial Invariant of Graphs On Orientable Surfaces

2001; Wiley; Volume: 83; Issue: 3 Linguagem: Inglês

10.1112/plms/83.3.513

1460-244X

Béla Bollobás, Oliver Riordan,

Advanced Operator Algebra Research

Proceedings of the London Mathematical SocietyVolume 83, Issue 3 p. 513-531 Articles A Polynomial Invariant of Graphs On Orientable Surfaces Béla Bollobás, Béla Bollobás bollobas@msci.memphis.edu Department of Mathematical Sciences, University of Memphis, Memphis, TN, 38152-6429 USA Trinity College, Cambridge, CB2 1TQSearch for more papers by this authorOliver Riordan, Oliver Riordan O.M.Riordan@dpmms.cam.ac.uk Trinity College, Cambridge, CB2 1TQSearch for more papers by this author Béla Bollobás, Béla Bollobás bollobas@msci.memphis.edu Department of Mathematical Sciences, University of Memphis, Memphis, TN, 38152-6429 USA Trinity College, Cambridge, CB2 1TQSearch for more papers by this authorOliver Riordan, Oliver Riordan O.M.Riordan@dpmms.cam.ac.uk Trinity College, Cambridge, CB2 1TQSearch for more papers by this author First published: 23 December 2016 https://doi.org/10.1112/plms/83.3.513Citations: 55AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Abstract We consider cyclic graphs, that is, graphs with cyclic orders at the vertices, corresponding to 2-cell embeddings of graphs into orientable surfaces, or combinatorial maps. We construct a three variable polynomial invariant of these objects, the cyclic graph polynomial, which has many of the useful properties of the Tutte polynomial. Although the cyclic graph polynomial generalizes the Tutte polynomial, its definition is very different, and it depends on the embedding in an essential way. 2000 Mathematical Subject Classification: 05C10. Citing Literature Volume83, Issue3November 2001Pages 513-531 RelatedInformation