Chromatic Number Calculator

Find the chromatic number (minimum colors needed) for various graph types.

Graph Type

Number of vertices (n)

Formula

chi(K_5) = 5

Complete graph requires n colors since every vertex is adjacent to all others.

Chromatic Number

chi(G) = 5

Vertices

5

Edges

10

Chromatic Bounds

Lower bound (clique number)omega ≤ chi

Brooks' Theoremchi ≤ Delta + 1

About Chromatic Number

The chromatic number chi(G) is the minimum number of colors needed to properly color vertices
A proper coloring assigns colors so no adjacent vertices share the same color
Computing chi(G) is NP-hard for general graphs
The fractional chromatic number provides a lower bound