ИСТИНА

In the focus of my talk is a generalization of the Tutte polynomial for vertex-weighted graphs, for which the coefficients of the “contraction-deletion” relation depend nontrivially on the vertex weights. We demonstrate that the corresponding coefficient relation coincides with the symmetric 2-cocycle relation in the group cohomology. We show that our construction is a natural generalization of the symmetrized chromatic Stanley polynomial and obtain a representation of our polynomial by summing over subgraphs. Finally, we demonstrate that our polynomial is an reach source for constructing 4invariants of graphs, which are very important in the knot theory. The report is based on a joint paper by B. Bychkov, A. Kazakov and D. Talalaev, The Tutte polynomial of graphs with weighted vertices and group cohomology.