Title: Combinatorics and topology of graphs on surfaces.

Abstract.
   Graphs on surfaces appear in many different parts of mathematics, physics, 
and science. In combinatorics they may be considered from a point of view of 
matroids. There are several matroids associated to a graph on surface. Various 
their parameters can be assembled into so called Las Vergnas polynomial. From 
the topological point of view circuits of the graph may be considered as 
elements on the first homology group of the surface. These topological parameters 
also can be assembled into a polynomial introduced recently by V.Krushkal. Both 
polynomials generalize the partition function of the Potts model in statistical 
physics. It turns out that the Las Vergnas polynomial is a specialization of the 
Krushkal one.
   I will briefly review an introduction to the matroid theory, define the two 
polynomials, and explain the relationship between them. Then I explain an 
importance of the Krushkal polynomial for the theory of knots and links.