Hamiltonicity conjecture for regular sublinear expanders

For ε>0\varepsilon>0, let an (ε,d)(\varepsilon,d)-expander be the sublinear-expansion notion used in the source. Hamiltonicity conjecture for regular sublinear expanders. There exists d0d_0 such that, for every dd0d\geq d_0, every dd-regular (ε,d)(\varepsilon,d)-expander contains a Hamilton cycle. The parser marks this conjecture as resolved by Draganić, Montgomery, Munhá Correia, Pokrovskiy and Sudakov.

Sources & referencesView supporting material

Primary source

Richard Montgomery, “Recent progress in graph theory using expansion”, arXiv:2607.26049 (2026).

Additional references

3 papers in this index state this conjecture (2024–2026). The statement above is taken from the most recent of them; the others are arXiv:2605.15043, arXiv:2402.06603.

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