On \(r\)-uniform linear hypergraphs with no Berge-\(K_{2,t}\)

Craig Timmons¹

¹California State University Sacramento

The electronic journal of combinatorics, Tome 24 (2017) no. 4

Résumé

Let $\mathcal{F}$ be an $r$-uniform hypergraph and $G$ be a multigraph. The hypergraph $\mathcal{F}$ is a Berge-$G$ if there is a bijection $f: E(G) \rightarrow E( \mathcal{F} )$ such that $e \subseteq f(e)$ for each $e \in E(G)$. Given a family of multigraphs $\mathcal{G}$, a hypergraph $\mathcal{H}$ is said to be $\mathcal{G}$-free if for each $G \in \mathcal{G}$, $\mathcal{H}$ does not contain a subhypergraph that is isomorphic to a Berge-$G$. We prove bounds on the maximum number of edges in an $r$-uniform linear hypergraph that is $K_{2,t}$-free. We also determine an asymptotic formula for the maximum number of edges in a linear 3-uniform 3-partite hypergraph that is $\{C_3 , K_{2,3} \}$-free.

Détail

DOI : 10.37236/6470

Classification : 05C65, 05C35, 05D99, 05C60
Mots-clés : hypergraph Turán problem, Sidon sets, Berge-\(K_{2,t}\)