# How to sample connected K-partitions of a graph

@article{Meil2018HowTS, title={How to sample connected K-partitions of a graph}, author={Marina Meilă}, journal={ArXiv}, year={2018}, volume={abs/1808.00050} }

A connected undirected graph $G=(V,E)$ is given. This paper presents an algorithm that samples (non-uniformly) a $K$ partition $U_1,\ldots U_K$ of the graph nodes $V$, such that the subgraph induced by each $U_k$, with $k=1:K$, is connected. Moreover, the probability induced by the algorithm over the set ${\mathcal C}_K$ of all such partitions is obtained in closed form.

## One Citation

### Empirical sampling of connected graph partitions for redistricting.

- MathematicsPhysical review. E
- 2021

This paper examines mixing times of a popular Glauber dynamics based Markov chain and shows how the self-avoiding walk phase transitions interact with mixing time, and analyzes the robustness of the qualitative properties of typical districting plans with respect to score functions and a certain lattice-like graph.

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The numbers C(G) and P (G) can be regarded as the (connected) graph analogs of the number of subsets and theNumber of set partitions, respectively, of an n-element set.