Non-matroidal generalizations

Abstract

This chapter covers several generalizations of the Tutte polynomial to combinatorial structures that are not matroids, including structures arising from trees, rooted graphs, posets, finite subsets of points in Euclidean space. In each case, the generalized Tutte polynomial encodes meaningful combinatorial information about the object under consideration. Defining a Tutte polynomial for a set with a rank function. Computing the Tutte polynomial using a deletion–contraction recursion. Application to greedoids, specialized to rooted graphs and digraphs. Application to antimatroids, specialized to trees, rooted trees and posets. The β-invariant for antimatroids, specialized to chordal graphs and finite subsets of Euclidean space.