The Tutte polynomial is a well-studied invariant of graphs and matroids. We first extend the
Tutte polynomial from graphs to hypergraphs, and more generally from matroids to …

In 1912, Birkhoff introduced the chromatic polynomial of a graph, which counts the number
of proper colorings of a graph. In 1995, Stanley introduced the chromatic symmetric function …

Using the combinatorics of-unimodal sets, we establish two new results in the theory of
quasisymmetric functions. First, we obtain the expansion of the fundamental basis into …

Graph invariants are a useful tool in graph theory. Not only do they encode useful
information about the graphs to which they are associated, but complete invariants can be …

The Tutte polynomial is an isomorphism invariant of graphs that generalizes the chromatic
and the flow polynomials. This two-variable polynomial with integral coefficients is known to …

Some polynomials find their way into chemical graph theory less often than others. They
could provide new ways of understanding the origins of regularities in the chemistry of …

The Weighted First-Order Model Counting Problem (WFOMC) asks to compute the weighted
sum of models of a given first-order logic sentence over a given domain. It can be solved in …

Employing a recent technology of tree surgery we prove a``deletion-constriction''formula for
products of rooted spanning trees on weighted directed graphs that generalizes deletion …

Determining whether two graphs are isomorphic is an important and difficult problem in
graph theory. One way to make progress towards this problem is by finding and studying …

Abstract Automata networks are a very general model of interacting entities, with
applications to biological phenomena such as gene regulation. In many contexts, the order …