Tootfinder

Nancy Mace’s gleeful endorsement of ICE’s courthouse ambushes on undocumented immigrants exposes her as a hypocritical opportunist who prioritizes performative cruelty over constitutional due process and American values of fairness
https://www.theguardian.com/us-news/2025/j

Cycle-factors of regular graphs via entropy
Micha Christoph, Nemanja Dragani\'c, Ant\'onio Gir\~ao, Eoin Hurley, Lukas Michel, Alp M\"uyesser
https://arxiv.org/abs/2507.19417

Cycle-factors of regular graphs via entropy
It is a classical result that a random permutation of $n$ elements has, on average, about $\log n$ cycles. We generalise this fact to all directed $d$-regular graphs on $n$ vertices by showing that, on average, a random cycle-factor of such a graph has $\mathcal{O}((n\log d)/d)$ cycles. This is tight up to the constant factor and improves the best previous bound of the form $\mathcal{O}(n/\sqrt{\log d})$ due to Vishnoi. Our results also yield randomised polynomial-time algorithms for finding su…