Polynomial invariants of graphs on surfaces
Combinatorics
2015-03-17 v2 Geometric Topology
Abstract
For a graph embedded into a surface, we relate many combinatorial parameters of the cycle matroid of the graph and the bond matroid of the dual graph with the topological parameters of the embedding. This will give an expression of the polynomial, defined by M.Las Vergnas in a combinatorial way using matroids as a specialization of the Krushkal polynomial, defined using the symplectic structure in the first homology group of the surface.
Cite
@article{arxiv.1012.5053,
title = {Polynomial invariants of graphs on surfaces},
author = {R. Askanazi and S. Chmutov and C. Estill and J. Michel and P. Stollenwerk},
journal= {arXiv preprint arXiv:1012.5053},
year = {2015}
}
Comments
to appear in Quantum Topology