On \(r\)-uniform linear hypergraphs with no Berge-\(K_{2,t}\)
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Publication:1684649
zbMath1376.05104arXiv1609.03401MaRDI QIDQ1684649
Publication date: 12 December 2017
Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)
Abstract: 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 $f: E(G)
ightarrow E( mathcal{F} )$ 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.
Full work available at URL: https://arxiv.org/abs/1609.03401
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Extremal problems in graph theory (05C35) Hypergraphs (05C65) Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) (05C60) Extremal combinatorics (05D99)
Cites Work
- Turán numbers of bipartite graphs plus an odd cycle
- Hypergraphs with no cycle of length 4
- 3-uniform hypergraphs avoiding a given odd cycle
- A counterexample to sparse removal
- On 3-uniform hypergraphs without a cycle of a given length
- Pentagons vs. triangles
- On hypergraphs of girth five
- New asymptotics for bipartite Turán numbers
- Hypergraph Extensions of the Erdős-Gallai Theorem
- The Maximum Number of Triangles in C2k+1-Free Graphs
- Hypergraphs with No Cycle of a Given Length
- Solving a linear equation in a set of integers I
- Linear Turán Numbers of Linear Cycles and Cycle-Complete Ramsey Numbers
- Extremal Results for Berge Hypergraphs
- Many \(T\) copies in \(H\)-free graphs
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