On a Conjecture of Thomassen
  In 1989, Thomassen asked whether there is an integer-valued function f(k) such that every f(k)-connected graph admits a spanning, bipartite $k$-connected subgraph. In this paper we take a first, humble approach, showing the conjecture is true up to a log n factor. 
Michelle Delcourt and Asaf Ferber
math.CO