---
tag: VXS0D789F1
kind: concept
name: Harmonious coloring
aliases: [harmonius-chromatic-number]
sources:
  - wikipedia: en:690728@r1152945582
    locator: Harmonious coloring
    note: adopted
    mention: wikipedia://en/690728
    sections: [Summary]
same_as:
  wikidata: Q5659354
  wikipedia: Harmonious coloring
inventory: [ERGJ5Y1R2K]
---

## Summary

In graph theory, a **harmonious coloring** is a (proper) vertex coloring in which every pair of colors appears on *at most* one pair of adjacent vertices. It is the opposite of the complete coloring, which instead requires every color pairing to occur *at least* once. The **harmonious chromatic number** $\chi_{H}(G)$ of a [[graph|00C0BR7D7H]] $G$ is the minimum number of colors needed for any harmonious coloring of $G$.