Mathematics Atlas

How Proof Is Made
Sign In
Text size
100%
Theme
Theorem

Vizing's Theorem

Combinatorics and Graph Theory

The edges of any simple graph can be properly colored using either the maximum vertex degree or one more than the maximum vertex degree, and never more, colors. Proved by Vadim Vizing, it is the foundational result of edge-coloring theory, splitting graphs cleanly into two classes.

Facts
Statement
Vizing's theorem states that every simple undirected graph may be edge colored using a number of colors that is at most one larger than the maximum degree of the graph. 1
Proof Year
1964 1
Classification
Statement Form
Uniqueness Theorem 1
Statement Form
Inequality 1
Connections

Has Statement Form

In Branch

Proved By

Source Vizing's Theorem (Wikipedia)
Sources
1. Vizing's Theorem (Wikipedia)
Wikimedia Foundation
  • lead paragraph, opening sentence
    In graph theory, Vizing's theorem states that every simple undirected graph may be edge colored using a number of colors that is at most one larger than the maximum degree Δ of the graph.
  • lead paragraph, sentence naming the publication year
    The theorem is named for Vadim G. Vizing who published it in 1964.
  • Proved By: Vadim G. Vizing, Lead section
    Vizing who published it in 1964.
  • In Group: Graph Theory, Lead section
    In graph theory, Vizing's theorem states that every simple undirected
View the Source
Comments (0)
No comments yet. Be the first to share a thought.
Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.