10:45

Robert Cori’s seminar

Joint work with G. Hetyei.
Associating a polynomial with a graph has been a way of providing an algebraic tool for studying combinatorial objects. As early as 1932, Hassler Whitney introduced coefficients on a graph that enable a two-variable polynomial to be defined. It can be used to calculate the number of colorations of this graph. William Tutte later used a change of variables to introduce a new polynomial that became more famous.
In 1980, Jean-Guy Penaud and I introduced a notion of refinement on hypergraphs (topological representation of hypergraphs), enabling us to look at hypertrees covering hypergraphs.
Very recently, we took up this notion with Gabor Hetyie to introduce a polynomial associated with a hypermap. When this hypermap is a map, this polynomial is the one introduced by Whitney for the graph represented by the map.
The aim of this presentation is to address the question we have been asking Gabor about the polynomial obtained by performing the same change of variables on our polynomial as that performed by W.Tutte.

Salle 76