A general notion of activity for the Tutte polynomial

Julien Courtiel (1)

1 SFU.ca - Simon Fraser University = Université Simon Fraser

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.

Mots clés: activities; Tutte polynomial

Domaines: Combinatoire [math.CO]

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