Graph coloring | Theorems in graph theory

Vizing's theorem

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.At least Δ colors are always necessary, so the undirected graphs may be partitioned into two classes: "class one" graphs for which Δ colors suffice, and "class two" graphs for which Δ + 1 colors are necessary.A more general version of Vizing's theorem states that every undirected multigraph without loops can be colored with at most Δ+µ colors, where µ is the multiplicity of the multigraph.The theorem is named for Vadim G. Vizing who published it in 1964. (Wikipedia).

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Graphs and Combinatorics | Dual graph | Kempe chain | Planar graph | Almost all | Platonic solid | Vadim G. Vizing | Total coloring | Brooks' theorem | Multigraph | Pseudoforest | Path (graph theory) | Degree (graph theory) | Torus | Snark (graph theory) | Disjoint union | Erdős–Rényi model | Graph theory | Induced subgraph | Bipartite graph | Cycle (graph theory) | Sphere | Four color theorem | Independent set (graph theory) | Journal of Combinatorial Theory | Branko Grünbaum | Graph embedding | Edge coloring