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We show that set cover on a universe of size $n$ and with sets of size at most $k$ can be solved in time $2^{(1-1/k+O(1/k^{3/2}))n}$. This improves on a $2^{(1-0.929/k)n}$-time algorithm of Bj\"orklund (STACS 2010) for all sufficiently large $k$.
We show that for all $k$, there exists $\varepsilon_k>0$ such that graph $k$-coloring can be solved by a randomized algorithm with one-sided error in time $O((2-\varepsilon_k)^n)$. Prior to this work and independent concurrent work of Zamir [arXiv, 2026], exponential improvements over the $2^n \cdot \mathrm{poly}(n)$-t...
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