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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…
math.CO2024
Ramsey multiplicity of apices of trees
Daniel Kráľ, Matjaž Krnc, Ander Lamaison
A graph is common if its Ramsey multiplicity, i.e., the minimum number of monochromatic copies of contained in any -edge-coloring of , is asymptotically the same as…