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.
- Dependent random choice
- Mader conjecture
- Topological minors
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics