Author

Levi Segal

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Preprint Sep 2026

Logarithmic Circumference In Tough Graphs

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.

Levi Segal, J. Verstraete · 1 citation