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Densities in large permutations and parameter testing
Roman Glebov, Carlos Hoppen, Tereza Klimosova +3
A classical theorem of Erdos, Lovasz and Spencer asserts that the densities of connected subgraphs in large graphs are independent. We prove an analogue of this theorem for permuta…
Comparable pairs in families of sets
Noga Alon, Shagnik Das, Roman Glebov +1
Given a family of subsets of , we say two sets are comparable if or . Sperner's celebrated theorem gives the si…
The threshold probability for long cycles
Roman Glebov, Humberto Naves, Benny Sudakov
For a given graph of minimum degree at least , let denote the random spanning subgraph of obtained by retaining each edge independently with probability .…
Infinite dimensional finitely forcible graphon
Roman Glebov, Tereza Klimosova, Daniel Kral
Graphons are analytic objects associated with convergent sequences of dense graphs. Finitely forcible graphons, i.e., those determined by finitely many subgraph densities, are of p…