A Tutte Polynomial for Maps
2018 ◽
Vol 27
(6)
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pp. 913-945
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Keyword(s):
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.
2001 ◽
Vol 83
(3)
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pp. 513-531
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2010 ◽
Vol 20
(2)
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pp. 267-287
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1993 ◽
Vol 113
(2)
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pp. 267-280
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1998 ◽
Vol 124
(1)
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pp. 21-49
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2005 ◽
Vol 14
(07)
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pp. 919-929
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Keyword(s):
2020 ◽
Vol 9
(10)
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pp. 8869-8881
1980 ◽
Vol 88
(1)
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pp. 15-31
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Keyword(s):