Mader conjectured that every -free graph has a subdivision of a clique of order linear in its average degree. We show that every -free graph has such a subdivision of a large clique.
We also prove the dense case of Mader's conjecture in a stronger sense, i.e., for every c, there is a such that every -free graph with average degree has a subdivision of a clique with where every edge is subdivided exactly 3 times
