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math.CO2026
The critical probability for percolation on finite graphs
Micha Christoph, Patryk Morawski, Yuval Wigderson
We determine the critical probability for Bernoulli bond percolation on essentially any finite graph. Namely, letting denote the spectral radius (maximum eigenvalue) of ,…
math.CO2026
Nearly tight bounds for induced subdivisions
Zach Hunter, Aleksa Milojević, Patryk Morawski +1
Subdivisions of complete graphs play a central role in combinatorics, having deep connections to structural, extremal, and topological aspects of graph theory. A celebrated conject…
math.CO2026
Ramsey number of a cycle versus a graph of a given size
Stijn Cambie, Andrea Freschi, Patryk Morawski +2
In this paper, we prove that for every and every graph with edges and no isolated vertices, the Ramsey number is at most ,…