Least number of infinite edges in non-bipartite hypergraph – mathoverflow.net

We call a hypergraph $H=(V,E)$ bipartite if there is $S\subseteq V$ with $e\cap S$ and $e\setminus S$ both nonempty for all $e\in E$. If $(\omega, E)$ is not bipartite and all members are infinite, do ...