New answers tagged hypergraph
5
votes
Accepted
Finite pair-splitting family of $\mathbb{N}$
$\newcommand\F{\mathfrak F}\newcommand\P{\mathfrak P}\newcommand\N{\mathbb N}\newcommand\om{\omega}$No. Let $\P$ be the partition of $\N$ generated by $\F$.
Detail: If $\F=\{S_1,\dots,S_n\}$, then the ...
- 110k
4
votes
Accepted
$\aleph_0$-uniform non-bipartite linear hypergraph
Every $\aleph_0$-uniform linear hypergraph is bipartite. More generally:
Theorem. If $H=(V,E)$ is an $\aleph_0$-uniform hypergraph, and if there is a number $n\lt\aleph_0$ such that $|\{e\in E:S\...
- 10.6k
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