Chromatic Number Calculator
Find the chromatic number (minimum colors needed) for various graph types.
Graph Type
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
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Editorial Note
MyCalcBuddy Editorial Team
This page is maintained as an educational calculator reference.
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Formula Source: Handbook of Mathematical Functions
by Abramowitz & Stegun
🔄Last reviewed: May 2026
✓Formula checks are based on standard references and internal QA review.