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
StatementVizing'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 Classification
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Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Sources
1. Vizing's Theorem (Wikipedia)
Wikimedia Foundationlead 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.
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