346 citations
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5 papers · 2 filters
On the number of H-free hypergraphs
Tao Jiang, Sean Longbrake
Two central problems in extremal combinatorics are concerned with estimating the number , the size of the largest -free hypergraph on vertices, and the number $forb…
Subgraphs with a positive minimum semidegree in digraphs with large outdegree
Andrzej Grzesik, Vojtech Rodl, Jan Volec
We prove that every -vertex directed graph with the minimum outdegree contains a subgraph satisfying \[ \min\left\{δ^+(H), δ^-(H) \right\} \ge \frac{d(d+1)}…
Longest cycles in vertex-transitive and highly connected graphs
Carla Groenland, Sean Longbrake, Raphael Steiner +2
We present progress on three old conjectures about longest paths and cycles in graphs. The first pair of conjectures, due to Lovász from 1969 and Thomassen from 1978, respectively,…
Tree Posets: Supersaturation, Enumeration, and Randomness
Tao Jiang, Sean Longbrake, Sam Spiro +1
We develop a powerful tool for embedding any tree poset of height in the Boolean lattice which allows us to solve several open problems in the area. We show that: * If …
The number of cliques in hypergraphs with forbidden subgraphs
Ayush Basu, Vojtech Rodl, Yi Zhao
We study the maximum number of -vertex cliques in -uniform hypergraphs not containing complete -partite hypergraphs . By using the hyperg…