3 papers
math.CO2026
Fundamental cycles in grid graphs
Bartłomiej Kielak, Daniel Král', Ander Lamaison +1
We show that the average length of a fundamental cycle with respect to any fixed spanning tree of the square grid is at least ; the bound is asymptotically t…
math.CO2026
Sidorenko property and forcing in regular tournaments
Daniel Král', Matjaž Krnc, Filip Kučerák +2
We give a complete characterization of tournaments H that have the Sidorenko property with respect to nearly regular tournaments, i.e., the homomorphism density of H among all near…
math.CO2025
Convergence of spectra of digraph limits
Jan Grebík, Daniel Král', Xizhi Liu +2
The relation between densities of cycles and the spectrum of a graphon, which implies that the spectra of convergent graphons converge, fundamentally relies on the self-adjointness…