On the inducibility of cycles

Dan Hefetz, Mykhaylo Tyomkyn

Research output: Contribution to journalArticlepeer-review


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)593-599
Number of pages7
JournalElectronic Notes in Discrete Mathematics
StatePublished - Aug 2017


  • Inducibility
  • cycles
  • extremal problems
  • multivariate optimisation


Dive into the research topics of 'On the inducibility of cycles'. Together they form a unique fingerprint.

Cite this