On the inducibility of cycles

Dan Hefetz, Mykhaylo Tyomkyn

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


In 1975 Pippenger and Golumbic proved that any graph on n vertices admits at most 2e(n/k)k induced k-cycles. This bound is larger by a multiplicative factor of 2e than the simple lower bound obtained by a blow-up construction. Pippenger and Golumbic conjectured that the latter lower bound is essentially tight. In the present paper we establish a better upper bound of (128e/81)⋅(n/k)k. This constitutes the first progress towards proving the aforementioned conjecture since it was posed.

Original languageEnglish
Pages (from-to)243-258
Number of pages16
JournalJournal of Combinatorial Theory. Series B
StatePublished - Nov 2018


  • Cycles
  • Enumeration
  • Inducibility
  • Large graphs


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