# A general notion of activity for the Tutte polynomial

Abstract : In the literature can be found several descriptions of the Tutte polynomial of graphs. Tutte defined it thanks to a notion of activity based on an ordering of the edges. Thereafter, Bernardi gave a non-equivalent notion of the activity where the graph is embedded in a surface. In this paper, we see that other notions of activity can thus be imagined and they can all be embodied in a same notion, the $\Delta$-activity. We develop a short theory which sheds light on the connections between the different expressions of the Tutte polynomial.
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https://hal.archives-ouvertes.fr/hal-01088871
Contributor : Julien Courtiel <>
Submitted on : Monday, December 1, 2014 - 5:22:25 PM
Last modification on : Thursday, November 8, 2018 - 3:46:04 PM
Document(s) archivé(s) le : Friday, April 14, 2017 - 11:23:27 PM

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• HAL Id : hal-01088871, version 1

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Julien Courtiel. A general notion of activity for the Tutte polynomial. 2014. ⟨hal-01088871⟩

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