In absence of long chordless cycles, large tree-width becomes a local phenomenon
Daniel Weißauer·2018-03-07·via math.CO updates on arXiv.org
We prove that, for all $\ell$ and $s$, every graph of sufficiently large tree-width contains either a complete bipartite graph $K_{s,s}$ or a chordless cycle of length greater than $\ell$.
