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A Tutte Polynomial for Maps

  • ANDREW GOODALL (a1), THOMAS KRAJEWSKI (a2), GUUS REGTS (a3) and LLUÍS VENA (a1) (a4)
Abstract

We follow the example of Tutte in his construction of the dichromate of a graph (i.e. the Tutte polynomial) as a unification of the chromatic polynomial and the flow polynomial in order to construct a new polynomial invariant of maps (graphs embedded in orientable surfaces). We call this the surface Tutte polynomial. The surface Tutte polynomial of a map contains the Las Vergnas polynomial, the Bollobás–Riordan polynomial and the Krushkal polynomial as specializations. By construction, the surface Tutte polynomial includes among its evaluations the number of local tensions and local flows taking values in any given finite group. Other evaluations include the number of quasi-forests.

Copyright
COPYRIGHT: © Cambridge University Press 2018 
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†

Supported by Project ERCCZ LL1201 Cores and the Czech Science Foundation, GA ČR 16-19910S.

‡

Supported by ANR grant ANR JCJC ‘CombPhysMat2Tens’.

§

Supported by the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement 339109, and by an NWO Veni grant.

Supported by the Center of Excellence–Institute for Theoretical Computer Science, Prague, P202/12/G061, and by Project ERCCZ LL1201 Cores.

‖

The research leading to these results received funding from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement 339109.

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