[2] In 2004 Kühn published a pair of papers in Combinatorica with her thesis advisor, Reinhard Diestel, concerning the cycle spaces of infinite graphs.
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.
"[4] In 2011, Kühn and her co-authors published a proof of Sumner's conjecture, that "every n-vertex polytree forms a subgraph of every (2n − 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".
[7] Together with Osthus, she was a recipient of the 2014 Whitehead Prize of the London Mathematical Society for "their many results in extremal graph theory and related areas.
[9] and appointed as a Royal Society Wolfson Research Merit Award holder in 2015.