81 citations · 836 across the 70 of their papers we have counts for
4 papers · 2 filters
Counting Hamilton cycles in Dirac hypergraphs
Stefan Glock, Stephen Gould, Felix Joos +2
A tight Hamilton cycle in a -uniform hypergraph (-graph) is a cyclic ordering of the vertices of such that every set of consecutive vertices in the ordering forms…
Path and cycle decompositions of dense graphs
António Girão, Bertille Granet, Daniela Kühn +1
We make progress on three long standing conjectures from the 1960s about path and cycle decompositions of graphs. Gallai conjectured that any connected graph on vertices can be…
Dirac's theorem for random regular graphs
Padraig Condon, Alberto Espuny Díaz, António Girão +2
We prove a `resilience' version of Dirac's theorem in the setting of random regular graphs. More precisely, we show that, whenever is sufficiently large compared to $\varepsilo…
Decompositions into isomorphic rainbow spanning trees
Stefan Glock, Daniela Kühn, Richard Montgomery +1
A subgraph of an edge-coloured graph is called rainbow if all its edges have distinct colours. Our main result implies that, given any optimal colouring of a sufficiently large com…