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math.CO2026
The Lovász Local Lemma Is Sharp for the Hat Guessing Number
Thomas Delépine, Matthieu Rosenfeld
In the hat guessing game on a graph , each vertex is occupied by a player wearing a hat whose color is chosen from a set of colors. Each player knows the graph and their pos…
cs.DM2026
The lonely runner conjecture holds for nine runners
Matthieu Rosenfeld
We prove that the lonely runner conjecture holds for nine runners. Our proof is based on a couple of improvements of the method we used to prove the conjecture for eight runners.