Edge cut splitting formulas for Tutte-Grothendieck invariants

Tutte-Grothendieck invariants of graphs are mappings from a class of graphs to a commutative ring that are characterized recursively by contraction-deletion rules. Well known examples are the Tutte, chromatic, tension and flow polynomials. Suppose that an edge cut C divides a graph C into two parts G(1), G'(1) and that G(1), G'(1) are the sets of minors of G whose edge sets consist of C and edges of G(1), G'(1), respectively. We study determinant formulas evaluating a Tutte-Grothendieck invariant of C from the Tutte-Grothendieck invariants of graphs from G(1) and G'(1) (C) 2017 Elsevier Inc. All rights reserved.