24 papers
Intervals of uniform Turán densities
Heng Li, Xizhi Liu, Oleg Pikhurko
We prove that the set of uniform Turán densities of possibly infinite families of -graphs contains a terminal interval: there exists such that $[1-…
The inducibility of 6-vertex graphs
Levente Bodnár, Jun Gao, Jared León +3
The inducibility constant of a graph is the asymptotically maximum induced density of in a growing sequence of graphs. This paper systematically investigates the c…
New bounds for the optimal density of covering single-insertion codes via the Turán density
Oleg Pikhurko, Oleg Verbitsky, Maksim Zhukovskii
We prove that the density of any covering single-insertion code over the -symbol alphabet cannot be smaller than for some positive real no…
Strong non-principality of positive codegree Turán density
Levente Bodnár, Jun Gao, Oleg Pikhurko +2
The \emph{minimum positive codegree} of a -graph is the minimum, over all -sets that lie in at least one edge, of the number of edges containing that…
Semi-inducibility of 4-vertex graphs
Levente Bodnár, Oleg Pikhurko
For a graph whose edges are coloured blue or red, the -semi-inducibility problem asks for the maximum, over all graphs of given order , of the number of injections fr…
A note on the Ratio and Inertia Bounds for the -Independence Number
Jun Gao, Jie Ma, Oleg Pikhurko
The -th power of a graph is the graph on the same vertex set where the edge set consists of those pairs of distinct vertices of that are at distance at most fr…