Odd-subdivision degree-boundedness conjecture

An odd subdivision of a graph $G$ is a graph obtained from $G$ by replacing each edge by a path of odd length. For a positive integer $s$, a graph is $K_{s,s}$-free if it contains no subgraph isomorphic to the complete bipartite graph $K_{s,s}$. Odd-subdivision degree-boundedness conjecture. For every bipartite graph $H$ and positive integer $s$, the $K_{s,s}$-free graphs with no induced odd subdivision of $H$ have bounded average degree. This would simultaneously strengthen the degree-boundedness theorem of Kuhn and Osthus and the paper's pivot-minor result; the conjecture is presented as open, and it would also imply the cited theorem of Scott and Seymour when restricted to bipartite $H$.