Relations for Skein-Type Graph Polynomials

The Penrose, Tutte, and circuit partition (a translation of the Martin polynomial) polynomials can all be viewed, in at least certain cases, as skein-type polynomials, i.e. those that are computed via local reconfigurations at the vertices. Furthermore, these polynomials are interrelated in ways that reveal properties of important classes of graphs such as Eulerian, planar, cubic, and bipartite graphs. These interrelations also mean that new results for one of these polynomials immediately yield new insights and valuations for the others. Since significant advances have been made recently for the circuit partition polynomials, we have new results for the Penrose and Tutte polynomials as well.