AI Networking Cookbook: Practical recipes for AI-assisted network automation and development
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We prove that every $n$-vertex $15$-tough graph contains a cycle of length $\Omega(n^{1/20})$.
For every real $t>0$, we prove that every $2$-connected $t$-tough graph contains a cycle of length at least $\ell$ whenever $n \leq \ell(1 + 1/t)^{\lfloor \ell/2\rfloor - 1}$. This establishes the logarithmic bound conjectured by Broersma, van den Heuvel, Jung, and Veldman.
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