32 citations · 98 across the 35 of their papers we have counts for
6 papers · 1 filter
On Kahn's basis conjecture
Matija Bucić, Matthew Kwan, Alexey Pokrovskiy +1
In 1991, Kahn made the following conjecture. For any -dimensional vector space and any array of bases of , it is possible to choose a representative vec…
Halfway to Rota's basis conjecture
Matija Bucić, Matthew Kwan, Alexey Pokrovskiy +1
In 1989, Rota made the following conjecture. Given bases in an -dimensional vector space , one can always find disjoint bases of , each contain…
Nearly-linear monotone paths in edge-ordered graphs
Matija Bucic, Matthew Kwan, Alexey Pokrovskiy +3
How long a monotone path can one always find in any edge-ordering of the complete graph ? This appealing question was first asked by Chvátal and Komlós in 1971, and has since…
Ramsey goodness of cycles
Alexey Pokrovskiy, Benny Sudakov
Given a pair of graphs and , the Ramsey number is the smallest such that every red-blue coloring of the edges of the complete graph contains a red copy of…
Decompositions into spanning rainbow structures
Richard Montgomery, Alexey Pokrovskiy, Benny Sudakov
A subgraph of an edge-coloured graph is called rainbow if all its edges have distinct colours. The study of rainbow subgraphs goes back more than two hundred years to the work of E…
Embedding rainbow trees with applications to graph labelling and decomposition
Richard Montgomery, Alexey Pokrovskiy, Benny Sudakov
A subgraph of an edge-coloured graph is called rainbow if all its edges have distinct colours. The study of rainbow subgraphs goes back more than two hundred years to the work of E…