---
tag: PKBRMWYYN7
kind: concept
name: Weak coloring
sources:
  - wikipedia: en:20505205@r1368614620
    locator: Weak coloring
    note: adopted
    mention: wikipedia://en/20505205
    sections: [Summary]
same_as:
  wikidata: Q7977939
  wikipedia: Weak coloring
inventory: [48XQR2WH3V]
---

## Summary

In graph theory, a **weak coloring** is a special case of a graph labeling. A weak $k$-coloring of a graph $G = (V, E)$ assigns a color $c(v) \in \{1, 2, ..., k$} to each vertex $v \in V$, such that each non-isolated vertex is adjacent to at least one vertex with different color. In notation, for each non-isolated $v \in V$, there is a vertex $u \in V$ with $\{u, v\} \in E$ and $c(u) \ne c(v)$.