A Whitney polynomial for hypermaps

We introduce a Whitney polynomial for hypermaps and use it to generalize the results connecting the circuit partition polynomial to the Martin polynomial and the results on several graph invariants

Exploring the Tutte–Martin connection

The Martin polynomial of an oriented Eulerian graph encodes information about families of cycles in the graph. This paper uses a transformation of the Martin polynomial that facilitates standard combinatorial manipulations. These manipulations result in several new identities for the Martin polynomial, including a differentiation formula. These identities are then applied to get new combinatorial interpretations for valuations of the Martin polynomial, revealing properties o