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math.PR2026
First-Order Laws for Random Geometric Graphs on the Torus
Simi Haber, Mostafa Mirabi, Saharon Shelah
Let be the random geometric graph generated by independent uniform points on the -dimensional torus, with adjacency defined by torus -distance at most $…
math.CO2026
On the most reliable graphs with fixed redundancy
Rotem Brand, Reuven Cohen, Simi Haber +1
The all-terminal reliability of a graph is the probability that remains connected when each edge fails independently with probability . For fixed and , the unifor…