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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…
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…
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…
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…
Closure property of contraction-depth of matroids
Marcin Brianski, Daniel Kral, Ander Lamaison
Contraction-depth is a matroid depth parameter analogous to tree-depth of graphs. We establish the matroid analogue of the classical graph theory result asserting that the tree…
The dimension of the region of feasible tournament profiles
Daniel Kral, Ander Lamaison, Magdalena Prorok +1
Erd\H os, Lovász and Spencer showed in the late 1970s that the dimension of the region of -vertex graph profiles, i.e., the region of feasible densities of -vertex graphs in…