Partitioning the power set of $[n]$ into $C_k$-free parts

Eben Blaisdell, András Gyárfás, Robert A. Krueger +1

We show that for $n\ge 3,n\ne 5$, in any partition of $\mathcal{P}(n)$, the set of all subsets of $[n]=\{1,2,\dots ,n\}$, into $2^{n-2}-1$ parts, some part must contain a triangl…