---
tag: TZT25G2YB3
kind: concept
name: Henson graph
sources:
  - wikipedia: en:49104628@r1280021819
    locator: Henson graph
    note: adopted
    mention: wikipedia://en/49104628
    sections: [Summary]
same_as:
  wikidata: Q25304614
  wikipedia: Henson graph
inventory: [C1VZ02V7CS]
---

## Summary

In graph theory, the **Henson graph** $G_{i}$ is an undirected infinite graph, the unique countable homogeneous graph that does not contain an $i$-vertex [[clique|0BYX1D7C2E]] but that does contain all $K_{i}$-free finite graphs as induced subgraphs. For instance, $G_{3}$ is a triangle-free graph that contains all finite triangle-free graphs.