Bipartitions of Highly Connected Tournaments
Jaehoon Kim, Daniela Kühn, Deryk Osthus · SIAM Journal on Discrete Mathematics · 2016
We show that if $T$ is a strongly $10^9k^6\log(2k)$-connected tournament, there exists a partition $A,B$ of $V(T)$ such that each of $T[A]$, $T[B]$, and $T[A,B]$ is strongly $k$-connected. This provides solutions to tournament analogues of two partition conjectures of Thomassen regarding highly connected graphs. We also discuss spanning linkages as well as nonseparating subdivisions in highly connected tournaments.