The coboundary polynomial 
is a bivariate graph polynomial which can be expressed
in terms of the Tutte polynomial 
of a graph 
by
 |
where 
is the connected component count and 
is the vertex count of a
graph 
(Martin and Reiner 2005; Ardila 2007).
The coboundary polynomial provides a particularly concise way of expression generating functions for the Tutte polynomial of a complete
graph 
or complete bipartite graph 
.
