5 papers
Tight Hamilton cycles in random hypergraphs
Peter Allen, Julia Böttcher, Yoshiharu Kohayakawa +1
We give an algorithmic proof for the existence of tight Hamilton cycles in a random r-uniform hypergraph with edge probability p=n^{-1+eps} for every eps>0. This partly answers a q…
Maximum planar subgraphs in dense graphs
Peter Allen, Jozef Skokan, Andreas Würfl
Kühn, Osthus and Taraz showed that for each γ>0 there exists C such that any n-vertex graph with minimum degree γn contains a planar subgraph with at least 2n-C edges. We find the…
Turan numbers for bipartite graphs plus an odd cycle
Peter Allen, Peter Keevash, Benny Sudakov +1
For an odd integer , let denote the family of all odd cycles of length at most and let denote the family of all odd cycle…
The chromatic thresholds of graphs
Peter Allen, Julia Böttcher, Simon Griffiths +2
The chromatic threshold delta_chi(H) of a graph H is the infimum of d>0 such that there exists C=C(H,d) for which every H-free graph G with minimum degree at least d|G| satisfies c…
Ramsey-goodness -- and otherwise
Peter Allen, Graham Brightwell, Jozef Skokan
A celebrated result of Chvátal, Rödl, Szemerédi and Trotter states (in slightly weakened form) that, for every natural number , there is a constant such that, for any conn…