3 papers
math.CO2026
Solution of uniform Turán's Tetrahedron Problem
Bartłomiej Kielak, Daniel Král, Ander Lamaison +3
Turán's Tetrahedron Problem asks to determine the Turán density of the complete hypergraph (tetrahedron). This problem, posed by Turán in 1941, is one of the most famou…
math.CO2024
Four-coloring Eulerian triangulations of the torus
Marcin Brianski, Daniel Kral, Ander Lamaison +1
Hutchinson, Richter and Seymour [J. Combin. Theory Ser. B 84 (2002), 225-239] showed that every Eulerian triangulation of an orientable surface that has a sufficiently high represe…
math.CO2024
Hypergraphs with uniform Turán density equal to 8/27
Frederik Garbe, Daniel Iľkovič, Daniel Kráľ +2
In the 1980s, Erdős and Sós initiated the study of Turán problems with a uniformity condition on the distribution of edges: the uniform Turán density of a hypergraph is the inf…