Abstract
Mader conjectured that every C4-free graph has a subdivision of a clique of order linear in its average degree. We show that every C6-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 c′ such that every C4-free graph with average degree cn1/2 has a subdivision of a clique Kℓ with ℓ=⌊c′n1/2⌋ where every edge is subdivided exactly 3 times.
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