In 2004 Kühn published a pair of papers in
Combinatorica with her thesis advisor, Reinhard Diestel, concerning the
cycle spaces of infinite graphs. In these graphs the appropriate generalizations of
cycles and
spanning trees hinge on a proper treatment of the
ends of the graph. Reviewer
R. Bruce Richter writes that "the results are extremely satisfactory, in the sense that standard theorems for finite graphs have perfect analogues" but that "there is nothing simple about any aspect of this work. It is a nice mix of graph-theoretic and topological ideas." In 2011, Kühn and her co-authors published a proof of
Sumner's conjecture, that "every
n-vertex
polytree forms a subgraph of every (2
n − 2)-vertex
tournament", for all but finitely many values of
n.
MathSciNet reviewer K. B. Reid wrote that their proof "is an important and welcome development in tournament theory". ==Awards and honours==