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Author

Micha Christoph

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Preprint Sep 2026

Thinning and sprinkling: from robust sampling to almost Hamiltonicity

We develop the thinning--sprinkling technique, a general method for proving robustness of graph properties under random vertex sampling. Using it, we show that random induced subgraphs of tough graphs, high-degree connected vertex-transitive graphs, and nearly regular sublinear expanders retain strong connectivity or e...

Micha Christoph, Zach Hunter, Benny Sudakov · 2 citations · ⚡1
Preprint Aug 2026

The critical probability for percolation on finite graphs

We determine the critical probability for Bernoulli bond percolation on essentially any finite graph. Namely, letting $\lambda(G)$ denote the spectral radius (maximum eigenvalue) of $G$, we prove that the critical probability is at $1/\lambda(G)$: above this probability there is typically a component of order $\Omega(\...

Micha Christoph, Patryk Morawski, Yuval Wigderson · 1 citation

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