---
tag: H44Q2E3BZR
kind: concept
name: Chi-bounded
aliases: [x-bounded, bounded]
sources:
  - wikipedia: en:56030164@r1365511033
    locator: Chi-bounded
    note: adopted
    mention: wikipedia://en/56030164
    sections: [Summary]
same_as:
  wikidata: Q48999677
  wikipedia: Chi-bounded
inventory: [7ZDTNDEFD2]
---

## Summary

In graph theory, a **$\chi$-bounded** (using the Greek letter chi) family $\mathcal{F}$ of graphs is one for which there is some function $f$ such that, for every integer $t$ the graphs in $\mathcal{F}$ with $t=\omega(G)$ (clique number) can be [[colored|0NCPXH194Y]] with at most $f(t)$ colors. The function $f(t)$ is called a **$\chi$-binding function** for $\mathcal{F}$. These concepts and their notations were formulated by András Gyárfás. The use of the Greek letter chi in the term $\chi$-bounded is based on the fact that the chromatic number of a graph $G$ is commonly denoted $\chi(G)$. An overview of the area can be found in a survey of Alex Scott and Paul Seymour.