Generalized rainbow Turán numbers of odd cycles

József Balogh, Michelle Delcourt, Emily Heath, Lina Li

Research output: Contribution to journalArticlepeer-review


Given graphs F and H, the generalized rainbow Turán number ex(n,F,rainbow-H) is the maximum number of copies of F in an n-vertex graph with a proper edge-coloring that contains no rainbow copy of H. B. Janzer determined the order of magnitude of ex(n,Cs,rainbow-Ct) for all s≥4 and t≥3, and a recent result of O. Janzer implied that ex(n,C3,rainbow-C2k)=O(n1+1/k). We prove the corresponding upper bound for the remaining cases, showing that ex(n,C3,rainbow-C2k+1)=O(n1+1/k). This matches the known lower bound for k even and is conjectured to be tight for k odd.

Original languageEnglish (US)
Article number112663
JournalDiscrete Mathematics
Issue number2
StatePublished - Feb 2022


  • Cycle
  • Rainbow
  • Turán

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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