TY - JOUR
T1 - Generalized rainbow Turán numbers of odd cycles
AU - Balogh, József
AU - Delcourt, Michelle
AU - Heath, Emily
AU - Li, Lina
N1 - 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.
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 -