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# Journal of Combinatorics

## Volume 5 (2014)

### Number 3

### Augmenting and preserving partition connectivity of a hypergraph

Pages: 271 – 289

DOI: http://dx.doi.org/10.4310/JOC.2014.v5.n3.a1

#### Authors

#### Abstract

Let $k$ be a positive integer. A hypergraph $H$ is $k$-partition-connected if for every partition $P$ of $V(H)$, there are at least $k(|P|-1)$ hyperedges intersecting at least two classes of $P$. In this paper, we determine the minimum number of hyperedges in a hypergraph whose addition makes the resulting hypergraph $k$-partition-connected. We also characterize the hyperedges of a $k$-partition-connected hypergraph whose removal will preserve $k$-partition-connectedness.