---
tag: 74Q7PRTKVM
kind: concept
name: Clique cover
aliases: [clique-cover-number, clique-cover-problem, clique-partition, clique-partition-problem]
sources:
  - wikipedia: en:17113364@r1321127633
    locator: Clique cover
    note: adopted
    mention: wikipedia://en/17113364
    sections: [Summary]
same_as:
  wikidata: Q1096734
  wikipedia: Clique cover
inventory: [MDDQM39AM8]
---

## Summary

In graph theory, a **clique cover** or **partition into cliques** of a given undirected graph is a collection of [[cliques|0BYX1D7C2E]] that cover the whole graph. Generally, this means all vertices must be covered, and the term clique edge cover is used when all edges must be covered. A **minimum clique cover** is a clique cover that uses as few cliques as possible. The minimum $k$ for which a clique cover exists is called the **clique cover number** of the given graph.