---
tag: DZE2XNC6JP
kind: concept
name: Cactus
sources:
  - wikipedia: en:325802@r1373839425
    locator: Glossary of graph theory, section C
    note: adopted
    mention: wikipedia://en/325802#OT9R
    sections: [Summary]
inventory: [N4EXWN4R8T]
---

## Summary

A cactus graph, cactus tree, cactus, or Husimi tree is a connected graph in which each edge belongs to at most one cycle. Its blocks are cycles or single edges. If, in addition, each vertex belongs to at most two blocks, then it is called a Christmas cactus.