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math.CO2026
Hadwiger--Nelson Problem for Typical Norms
Noga Alon, Matija Bucić, James Davies
The classical Hadwiger-Nelson problem asks for the chromatic number of the unit distance graph of the Euclidean plane. Over the years, this problem has been considered for a variet…
math.CO2026
The uniform Turán density of the tetrahedron
Matija Bucić
We prove that the uniform Turán density of is equal to . Kielak, Král', Lamaison, Liu, Shu, and Wu have recently proved the same result using combinatorial methods…
math.CO2026
Long cycles in vertex transitive digraphs
Matija Bucić, Kevin Hendrey, Bojan Mohar +2
One of the most well-known conjectures concerning Hamiltonicity in graphs asserts that any sufficiently large connected vertex transitive graph contains a Hamilton cycle. In this f…