Construction of Directed 2K Graphs

In 2001, Komlós, Sárközy and Szemerédi proved that, for each α > 0, there is some c > 0 and n 0 such that, if n ≥ n 0, then every n-vertex graph with minimum degree at least ( 1 / 2 + α ) n contains a copy of every n-vertex tree with ...

In the nineties, Komlós, Sárközy and Szemerédi confirmed a conjecture of Bollobás, showing that for every positive α, Δ and sufficiently large n, every graph with minimum degree (1/2 + α)n contains every tree of order n and maximum degree at most ...

Let H be a fixed directed graph on h vertices, let G be a directed graph on n vertices and suppose that at least ε n² edges have to be deleted from it to make it H-free. We show that in this case G contains at least f(ε,H) n^h copies of H. This is proved ...