OPENHARDgraph theoryextremal graph theory
Let $G$ be a graph with $n$ vertices and $kn$ edges, and $a_1<a_2<\cdots$ the lengths of cycles in $G$. Is $\sum 1/a_i$ minimised when $G$ is a complete bipartite graph?
Notes: Liu and Montgomery established the asymptotically sharp lower bound >= (1/2 - o(1)) log k. Montgomery et al. have forthcoming work proving the bipartite graph is optimal for large k.
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