7 papers
Vertex Ramsey properties of randomly perturbed graphs
Shagnik Das, Patrick Morris, Andrew Treglown
Given graphs and , we say that is -Ramsey if every red/blue vertex colouring of containsa red copy of or a blue copy of . Results of Åuczak, RuciÅ…
Cycle tilings and -factors in directed graphs
Theodore Molla, Andrew Treglown
We prove several results concerning cycle tilings and -factors in digraphs. We provide a minimum semi-degree condition for forcing a digraph to contain a given spanning collecti…
Powers of Hamilton cycles in oriented and directed graphs
Louis DeBiasio, Jie Han, Allan Lo +3
The Pósa--Seymour conjecture determines the minimum degree threshold for forcing the th power of a Hamilton cycle in a graph. After numerous partial results, Komlós, Sárközy…
Ramsey-type problems for tilings in dense graphs
József Balogh, Andrea Freschi, Andrew Treglown
Given a graph , the Ramsey number is the smallest positive integer such that every -edge-colouring of yields a monochromatic copy of . We write to de…
Colour-bias perfect matchings in hypergraphs
Hiêp Hà n, Richard Lang, João Pedro Marciano +4
We study conditions under which an edge-coloured hypergraph has a particular substructure that contains more than the trivially guaranteed number of monochromatic edges. Our main r…
Arbitrary orientations of Hamilton cycles in directed graphs of large minimum degree
Louis DeBiasio, Andrew Treglown
In 1960, Ghouila-Houri proved that every strongly connected directed graph on vertices with minimum degree at least contains a directed Hamilton cycle. We asymptoticall…