---
tag: CKK800ERR1
kind: concept
name: Domatic number
aliases: [domatic-number-problem, domatic-partition]
sources:
  - wikipedia: en:1771980@r1326501538
    locator: Domatic number
    note: adopted
    mention: wikipedia://en/1771980
    sections: [Summary]
same_as:
  wikidata: Q3343067
  wikipedia: Domatic number
inventory: [TV1AERB9GG]
---

## Summary

In graph theory, a **domatic partition** of a [[graph|00C0BR7D7H]] $G = (V,E)$ is a [[partition|08QMKTWF9T]] of $V$ into disjoint sets $V_1$, $V_2$,...,$V_K$ such that each *V<sub>i</sub>* is a dominating set for *G*. The figure on the right shows a domatic partition of a graph; here the dominating set $V_1$ consists of the yellow vertices, $V_2$ consists of the green vertices, and $V_3$ consists of the blue vertices.