3 papers
math.CO2024
The dimension of the feasible region of pattern densities
Frederik Garbe, Daniel Kral, Alexandru Malekshahian +1
A classical result of ErdÅs, Lovász and Spencer from the late 1970s asserts that the dimension of the feasible region of densities of graphs with at most k vertices in large grap…
math.CO2024
Non-bipartite k-common graphs
Daniel Kral, Jonathan A. Noel, Sergey Norin +2
A graph H is k-common if the number of monochromatic copies of H in a k-edge-coloring of K_n is asymptotically minimized by a random coloring. For every k, we construct a connected…
math.CO2024
Common graphs with arbitrary chromatic number
Daniel Kral, Jan Volec, Fan Wei
Ramsey's Theorem guarantees for every graph H that any 2-edge-coloring of a sufficiently large complete graph contains a monochromatic copy of H. In 1962, Erdos conjectured that th…