Improved upper bounds for self-avoiding walks in .
Inequalities of Bonferroni-Galambos type with applications to the Tutte polynomial and the chromatic polynomial.
Bonferroni-Galambos inequalities for partition lattices.
A new two-variable generalization of the chromatic polynomial.
Bipartition Polynomials, the Ising Model, and Domination in Graphs
This paper introduces a trivariate graph polynomial that is a common generalization of the domination polynomial, the Ising polynomial, the matching polynomial, and the cut polynomial of a graph. This new graph polynomial, called the bipartition polynomial, permits a variety of interesting representations, for instance as a sum ranging over all spanning forests. As a consequence, the bipartition polynomial is a powerful tool for proving properties of other graph polynomials and graph invariants....
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