14 citations · 41 across the 10 of their papers we have counts for
9 papers · 1 filter
The codegree threshold of
Victor Falgas-Ravry, Oleg Pikhurko, Emil R. Vaughan +1
The codegree threshold of a -graph is the minimum such that every -graph on vertices in which every pair of vertices is contained in at…
The codegree threshold for 3-graphs with independent neighbourhoods
Victor Falgas-Ravry, Edward Marchant, Oleg Pikhurko +1
Given a family of 3-graphs , we define its codegree threshold to be the largest number such that there exists an -vertex 3-graph in which every…
Minimum Number of k-Cliques in Graphs with Bounded Independence Number
Oleg Pikhurko, Emil R. Vaughan
Erdos asked in 1962 about the value of f(n,k,l), the minimum number of k-cliques in a graph of order n and independence number less than l. The case (k,l)=(3,3) was solved by Lorde…
Turán H-densities for 3-graphs
Victor Falgas-Ravry, Emil R. Vaughan
Given an -graph on vertices, and a family of forbidden subgraphs, we define $\ex_{H}(n, \mathcal{F})$ to be the maximum number of induced copies of in…
On applications of Razborov's flag algebra calculus to extremal 3-graph theory
Victor Falgas-Ravry, Emil R. Vaughan
In this paper, we prove several new Turán density results for 3-graphs with independent neighbourhoods. We show: π(K_4^-, C_5, F_{3,2})=12/49, π(K_4^-, F_{3,2})=5/18, and π(J_4, F_…
An analogue of Ryser's Theorem for partial Sudoku squares
P. J. Cameron, A. J. W. Hilton, E. R. Vaughan
In 1956 Ryser gave a necessary and sufficient condition for a partial latin rectangle to be completable to a latin square. In 1990 Hilton and Johnson showed that Ryser's condition…