A correlation inequality involving stable set and chromatic polynomials
Journal of Combinatorial Theory Series B
A characterization of Tutte invariants of 2-polymatroids
Journal of Combinatorial Theory Series B
The Combinatorics of Network Reliability
The Combinatorics of Network Reliability
| Hi-index | 0.00 |
We develop a Tutte decomposition theory for matrices and their combinatorial abstractions, bimatroids. As in the graph or matroid case, this theory is based on a deletion-contraction decomposition. The contribution from the deletion, derived by an inclusion-exclusion argument, consists of three terms. With one more term contributed from the contraction, the decomposition has four terms in general. There are universal decomposition invariants, one of them being a corank-nullity polynomial. Under a simple change of variables, the corank-nullity polynomial equals a weighted characteristic polynomial. This gives an analog of an identity of Tutte. Applications to counting and critical problems on matrices and graphs are given.