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Mathematische Annalen

, Volume 323, Issue 1, pp 81–96 | Cite as

A polynomial of graphs on surfaces

  • Béla Bollobás
  • Oliver Riordan
Original article

ribbon graphs

, i.e., graphs realized as disks (vertices) joined together by strips (edges) glued to their boundaries, corresponding to neighbourhoods of graphs embedded into surfaces. We construct a four-variable polynomial invariant of these objects, the ribbon graph polynomial, which has all the main properties of the Tutte polynomial. Although the ribbon graph polynomial extends the Tutte polynomial, its definition is very different, and it depends on the topological structure in an essential way.

Mathematics Subject Classification (1991): 05C10 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Béla Bollobás
    • 1
  • Oliver Riordan
    • 2
  1. 1.Department of Mathematical Sciences, University of Memphis, Memphis TN 38152, USA (e-mail: bollobas@msci.memphis.edu) US
  2. 2.Trinity College, Cambridge CB2 1TQ, UK (e-mail: O.M.Riordan@dpmms.cam.ac.uk) UK

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