## Kristóf Bérczi:

Network flows and applications

Network flow theory provides a basic tool to treat conveniently
various graph characterization and optimization problems, including
the degree-constrained subgraph problem in a bipartite graph. Another
general framework in graph optimization is matroid theory. For
example, the problem of extending *k* given subtrees of a graph to *k*
disjoint spanning trees can be solved with the help of matroids. A
common generalization of these two big branches of combinatorial
optimization is the theory of submodular flows, initiated by Edmonds
and Giles. This covers not only the basic results on maximum flows
and min-cost circulations from network flow theory and weighted
matroid intersection from matroid theory, but also helps solving
significantly more complex graph optimization problems. In this
minicourse, we give an overview of the most fundamental results and
techniques of this area.