论文标题
广义的彩虹图恩数奇数循环
Generalized rainbow Turán numbers of odd cycles
论文作者
论文摘要
给定的图形$ f $和$ h $，通用的彩虹turán编号$ \ text {ex}（n，f，f，f，\ text {rainbow-} h）$是$ n $ vertex图中$ f $的最大副本数量，其中包含适当的边缘色，其中包含$ h $ $ h $的彩虹副本。 B. Janzer确定了$ \ text {ex}（n，c_s，\ text {rainbow-} c_t）$的数量级，用于所有$ s \ geq 4 $和$ t \ geq 3 $，以及O. Janzer的最新结果暗示了这一点$ \ text {ex}（n，c_3，\ text {rainbow-} c_ {2k}）= o（n^{1+1/k}）$。我们证明了其余情况下的相应上限，表明$ \ text {ex}（n，c_3，\ text {rainbow-} c_ {2k+1}）= o（n^{1+1/k}）$。这与已知的下限符合$ k $的均匀，并以$ k $奇数的形式猜想。
Given graphs $F$ and $H$, the generalized rainbow Turán number $\text{ex}(n,F,\text{rainbow-}H)$ 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 $\text{ex}(n,C_s,\text{rainbow-}C_t)$ for all $s\geq 4$ and $t\geq 3$, and a recent result of O. Janzer implied that $\text{ex}(n,C_3,\text{rainbow-}C_{2k})=O(n^{1+1/k})$. We prove the corresponding upper bound for the remaining cases, showing that $\text{ex}(n,C_3,\text{rainbow-}C_{2k+1})=O(n^{1+1/k})$. This matches the known lower bound for $k$ even and is conjectured to be tight for $k$ odd.
