7 papers
Hypergraph Ramsey numbers with quasipolynomial growth rate
Xiaoyu He, Jiaxi Nie, Logan Post +1
For a 3-uniform hypergraph (3-graph) , let be the smallest such that any -vertex -free 3-graph has an independent set of size . We construct a -graph $H…
Large point-line matchings and small Nikodym sets
Zach Hunter, Cosmin Pohoata, Jacques Verstraete +1
For any integer and prime power , we construct unexpectedly large induced matchings in the point-line incidence graph of by leveraging a new conn…
A question of ErdÅs and Graham on Egyptian fractions
David Conlon, Jacob Fox, Xiaoyu He +4
Answering a question of ErdÅs and Graham, we show that for each fixed positive rational number the number of ways to write as a sum of reciprocals of distinct positive int…
Independent Sets in Hypergraphs
Jacques Verstraete, Chase Wilson
A theorem of Shearer states that every -vertex triangle-free graph of maximum degree contains an independent set of size at least $(d\log d - d + 1)/(d - 1)^2 \cdot n…
When are off-diagonal hypergraph Ramsey numbers polynomial?
David Conlon, Jacob Fox, Benjamin Gunby +5
A natural open problem in Ramsey theory is to determine those -graphs for which the off-diagonal Ramsey number grows polynomially with . We make substan…
Improved bounds for the minimum degree of minimal multicolor Ramsey graphs
Yamaan Attwa, Sam Mattheus, Tibor Szabó +1
We provide two novel constructions of edge-disjoint -free graphs on the same vertex set, each of which has the property that every small induced subgraph contains a co…