Subdivisions of a large clique in C6-free graphs

József Balogh, Hong Liu, Maryam Sharifzadeh

Research output: Contribution to journalArticlepeer-review


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 K with ℓ=⌊c'n1/2⌋ where every edge is subdivided exactly 3 times.

Original languageEnglish (US)
Pages (from-to)18-35
Number of pages18
JournalJournal of Combinatorial Theory. Series B
StatePublished - May 1 2015


  • Dependent random choice
  • Girth
  • Mader conjecture
  • Subdivisions
  • Topological minors

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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