1 research outputs found
Recognising Graphic and Matroidal Connectivity Functions
A {\em connectivity function} on a set is a function
such that , that
for all , and that for all .
Graphs, matroids and, more generally, polymatroids have associated connectivity
functions. In this paper we give a method for identifying when a connectivity
function comes from a graph. This method uses no more than a polynomial number
of evaluations of the connectivity function. In contrast, we show that the
problem of identifying when a connectivity function comes from a matroid cannot
be solved in polynomial time. We also show that the problem of identifying when
a connectivity function is not that of a matroid cannot be solved in polynomial
time