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Generalized Rainbow Tur'an Numbers of Odd Cycles | | József Balogh
; Michelle Delcourt
; Emily Heath
; Lina Li
; | | Date: |
27 Oct 2020 | | Abstract: | Given graphs $F$ and $H$, the generalized rainbow Tur’an number
$ ext{ex}(n,F, ext{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
$ ext{ex}(n,C_s, ext{rainbow-}C_t)$ for all $sgeq 4$ and $tgeq 3$, and a
recent result of O. Janzer implied that
$ ext{ex}(n,C_3, ext{rainbow-}C_{2k})=O(n^{1+1/k})$. We prove the
corresponding upper bound for the remaining cases, showing that
$ ext{ex}(n,C_3, ext{rainbow-}C_{2k+1})=O(n^{1+1/k})$. This matches the known
lower bound for $k$ even and is conjectured to be tight for $k$ odd. | | Source: | arXiv, 2010.14609 | | Services: | Forum | Review | PDF | Favorites | |
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