A Tutte polynomial for maps II: The non-orientable case

We construct a new polynomial invariant of maps (graphs embedded in a closed surface, orientable or non-orientable), which contains as specializations the Krushkal polynomial, the Bollobás—Riordan polynomial, the Las Vergnas polynomial, and their extensions to non-orientable surfaces, and hence in p...

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Bibliographic Details
Published inEuropean journal of combinatorics Vol. 86; p. 103095
Main Authors Goodall, Andrew, Litjens, Bart, Regts, Guus, Vena, Lluís
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.05.2020
Online AccessGet full text
ISSN0195-6698
DOI10.1016/j.ejc.2020.103095

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Summary:We construct a new polynomial invariant of maps (graphs embedded in a closed surface, orientable or non-orientable), which contains as specializations the Krushkal polynomial, the Bollobás—Riordan polynomial, the Las Vergnas polynomial, and their extensions to non-orientable surfaces, and hence in particular the Tutte polynomial. Other evaluations include the number of local flows and local tensions taking non-identity values in a given finite group.
ISSN:0195-6698
DOI:10.1016/j.ejc.2020.103095