On decomposing a hypergraph into k connected sub-hypergraphs

A famous result by Rödl, Ruciński, and Szemerédi guarantees a (tight) Hamilton cycle in k-uniform hypergraphs H on n vertices with minimum ( k − 1 )-degree δ k − 1 ( H ) ⩾ ( 1 / 2 + o ( 1 ) ) n, thereby extending Dirac's result from ...

Fix a hypergraph $\mathcal{F}$. A hypergraph $\mathcal{H}$ is called a Berge copy of $\mathcal{F}$ or Berge-$\mathcal{F}$ if we can choose a subset of each hyperedge of $\mathcal{H}$ to obtain a copy of $\mathcal{F}$. A hypergraph $\mathcal{H}$ is Berge-$\mathcal{F}$-free if it does not contain a subhypergraph which is Berge copy of $\mathcal{F}$. This ...$\mathcal{}$$\mathcal{}$$\mathcal{}$$\mathcal{}$${}^{}$$\mathcal{}$

The edge-connectivity of a connected graph or hypergraph is the minimum number of edges whose removal renders the graph or hypergraph, respectively, disconnected. The edge-connectivity of a (hyper) graph cannot exceed its minimum degree. For graphs, ...