---
tag: 2DB1C700DZ
kind: concept
name: T-coloring
aliases: [t-colorings]
sources:
  - wikipedia: en:38341734@r1261521643
    locator: T-coloring
    note: adopted
    mention: wikipedia://en/38341734
    sections: [Summary]
same_as:
  wikidata: Q7667902
  wikipedia: T-coloring
inventory: [XY0E8WVVV4]
---

## Summary

In graph theory, a ***T*-Coloring** of a graph $G = (V, E)$, given the [[set|0BSJ7RQ9BW]] *T* of nonnegative integers containing 0, is a function $c: V(G) \to \mathbb{N}$ that maps each vertex to a positive [[integer|0C4JS9RF5M]] ([[color|0NCPXH194Y]]) such that if *u* and *w* are adjacent then $|c(u) - c(w)| \notin T$. In simple words, the [[absolute value|0FFXKTKKQC]] of the difference between two colors of adjacent vertices must not belong to fixed set *T*. The concept was introduced by William K. Hale. If *T* = $\{0\}$ it reduces to common vertex coloring.