Sean Longbrake

collaborators

12 papers

math.CO2026

Rational exponents near 3/2

Tao Jiang, Sean Longbrake, Liana Yepremyan

Given a graph $H$ , the extremal number $e x (n, H)$ is the maximum number of edges in an $n$ -vertex graph not containing $H$ as a subgraph. The well-known rational exponents conjectur…

math.CO2026

On the generalized TurÃ¡n number of complete bipartite graphs

Oliver Janzer, Sean Longbrake, Liana Yepremyan

For graphs $F$ and $H$ , the generalized TurÃ¡n number $ex (n, F, H)$ denotes the maximum number of copies of $F$ in an $H$ -free graph on $n$ vertices. We prove that if $s\in…

math.CO2026

Fractional hypergraph coloring

Margarita Akhmejanova, Sean Longbrake

We investigate proper $(a : b)$ -fractional colorings of $n$ -uniform hypergraphs, which generalize traditional integer colorings of graphs. Each vertex is assigned $b$ distinct colors…

math.CO2026

Induced rational exponents near two

Tao Jiang, Sean Longbrake

Given a bipartite graph $H$ and a natural number $s$ , let $ex^{*} (n, H, s)$ denote the maximum number of edges in an $n$ -vertex graph that contains neither $K_{s, s}$ nor an in…

math.CO2026

Random TurÃ¡n Problems for Graphs with a Vertex Complete to One Part

Sean Longbrake, Sam Spiro

Given a graph $F$ , the random TurÃ¡n problem asks to determine the maximum number of edges in an $F$ -free subgraph of $G_{n, p}$ . Prior to this work, the only bipartite graphs $F$ w…

math.CO2026

On the number of families avoiding a subposet

Tao Jiang, Sean Longbrake, Liana Yepremyan

In this paper we show that for any poset $P$ that is not an antichain, the number of induced $P$ -free families in the Boolean lattice $2^{[n]}$ is at most $ 2^{O(\mathrm{La}^*(n,P)…