TY - JOUR

T1 - Generalized rainbow Turán numbers of odd cycles

AU - Balogh, József

AU - Delcourt, Michelle

AU - Heath, Emily

AU - Li, Lina

N1 - Funding Information:
Research supported by NSF RTG Grant DMS-1937241, NSF Grant DMS-1764123, Arnold O. Beckman Research Award (UIUC Campus Research Board RB 18132), the Langan Scholar Fund (UIUC), and the Simons Fellowship.Research supported by NSERC under Discovery Grant No. 2019-04269 and an AMS-Simons Travel Grant.Research supported by NSF RTG Grant DMS-1937241.
Publisher Copyright:
© 2021 Elsevier B.V.

PY - 2022/2

Y1 - 2022/2

N2 - 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.

AB - 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.

KW - Cycle

KW - Rainbow

KW - Turán

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U2 - 10.1016/j.disc.2021.112663

DO - 10.1016/j.disc.2021.112663

M3 - Article

AN - SCOPUS:85117190119

SN - 0012-365X

VL - 345

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 2

M1 - 112663

ER -