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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…
math.CO2026
Pairs of square-free arithmetic progressions in infinite words
Thomas Delépine, Pascal Ochem, Matthieu Rosenfeld
We study a question of Harju from 2019 regarding the existence of infinite ternary square-free words whose subsequences modulo and are also square-free for relatively prime…
math.CO2026
Between proper and square coloring of planar graphs, hardness and extremal graphs
Thomas Delépine
-coloring is the problem of partitioning the vertex set of a graph into independent sets and 2-independent sets. This problem was recently introduced by Choi an…