---
tag: ZZH60KP9WQ
kind: concept
name: Bramble (graph theory)
sources:
  - wikipedia: en:36601188@r1335654220
    locator: Bramble (graph theory)
    note: adopted
    mention: wikipedia://en/36601188
    sections: [Summary]
same_as:
  wikidata: Q4956109
  wikipedia: Bramble (graph theory)
inventory: [RR7667SGXJ]
---

## Summary

In graph theory, a **bramble** for an undirected graph $G$ is a family of connected subgraphs of $G$ that all touch each other: for every pair of [[disjoint|0W4RPA8QH3]] subgraphs, there must exist an edge in $G$ that has one endpoint in each subgraph. The *order* of a bramble is the smallest size of a hitting set, a set of vertices of $G$ that has a nonempty intersection with each of the subgraphs. Brambles may be used to characterize the treewidth of $G$.