7 papers
A proof of Andersen's rainbow path conjecture for large
Candida Bowtell, Richard Montgomery, Alp Müyesser +1
We show that, for sufficiently large , every properly edge-coloured -vertex complete graph contains a path with vertices which uses each colour at most once (that is, a…
Nearly-uniform degree distributions in spanning subgraphs
Richard Montgomery, Alexey Pokrovskiy, Benny Sudakov
We show that, when , every -regular -vertex graph contains a spanning subgraph whose degree distribution is nearly uniform, i.e., for each , there are…
Towards Graham's rearrangement conjecture via rainbow paths
Matija BuciÄ, Bryce Frederickson, Alp Müyesser +2
We study an old question in combinatorial group theory which can be traced back to a conjecture of Graham from 1971. Given a group , and some subset , is it poss…
Chi-boundedness of graphs containing no cycles with chords
Joonkyung Lee, Shoham Letzter, Alexey Pokrovskiy
We prove that the family of graphs containing no cycle with exactly -chords is -bounded, for large enough or of form with an integer. This ve…
Decomposing cubic graphs into isomorphic linear forests
Gal Kronenberg, Shoham Letzter, Alexey Pokrovskiy +1
A common problem in graph colouring seeks to decompose the edge set of a given graph into few similar and simple subgraphs, under certain divisibility conditions. In 1987 Wormald c…
Size-Ramsey numbers of tight paths
Shoham Letzter, Alexey Pokrovskiy, Liana Yepremyan
The -colour size-Ramsey number of a hypergraph is the minimum number of edges in a hypergraph whose every -edge-colouring contains a monochromatic copy of . We sho…