Research Interests

Matching Theory

There exists an analogue of the theory of graph minors for graphs with perfect matchings. In particular one can generalise the notion of treewidth to this setting. I am interested to see how much of the graph minor theory developed by Robertson and Seymour can be replicated in the setting of matching covered (bipartite) graphs.

Topics I am interested in include

  • the perfect matching width of bipartite matching covered graphs, in particular characterisations, duality theorems and unavoidable matching minors,

  • the matching chromatic number, a generalisation of the dichromatic number, and

  • Pfaffian orientations and their relation to non-even (bi)directed graphs.

Structural Digraph Theory

The study of forbidden minors for undirected graphs has given rise to many nice and powerful results. The directed analogue however appears to be underdeveloped. One big reason behind this seems to be a severe lack of methods to handle the unavoidable antichains that occur in the study of so called butterfly minors. My aim here is to adapt and develop new methods in order to help establish a richer theory of minors for directed graphs.

Topics I am interested in include

  • directed treewidth, in particular characterisations, duality theorems and unavoidable butterfly minors,

  • the dichromatic number, and

  • the structure of directed cycles, in particular cycle packings and colouring the directed cycles of a digraph.

© 2019 by Sebastian Wiederrecht.