49 citations · 158 across the 33 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…
Dense induced bipartite subgraphs in triangle-free graphs
Matthew Kwan, Shoham Letzter, Benny Sudakov +1
The problem of finding dense induced bipartite subgraphs in -free graphs has a long history, and was posed 30 years ago by Erdős, Faudree, Pach and Spencer. In this paper, we ob…
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…
Anticoncentration for subgraph statistics
Matthew Kwan, Benny Sudakov, Tuan Tran
Consider integers such that . Given a large graph , what is the fraction of -vertex subsets of which span exactly edges? When $G…
Hypergraph cuts above the average
David Conlon, Jacob Fox, Matthew Kwan +1
An r-cut of a k-uniform hypergraph H is a partition of the vertex set of H into r parts and the size of the cut is the number of edges which have a vertex in each part. A classical…