Generalized rainbow Turan numbers of odd cycles

Given graphs F and H, the generalized rainbow Turan 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, C-s, rainbow-C-t) for all s >= 4 and t >= 3, and a recent result of O. Janzer implied that ex(n, C3, rainbow-C-2k) = O(n(1+1/k)). We prove the corresponding upper bound for the remaining cases, showing that ex(n, C-3, rainbow-C2k+1) = O(n(1+1/k)). This matches the known lower bound for k even and is conjectured to be tight for k odd. (c) 2021 Elsevier B.V. All rights reserved.