In a partial proper edge colouring with one uncoloured edge incident with a vertex , a Vizing fan is a sequence of neighbours of whose incident edge colours are missing at earlier fan vertices. With one more colour than the maximum degree, fan rotations and a two-colour Kempe chain free one common colour at the endpoints of the uncoloured edge.
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Vizing's theorem is a result in graph theory that relates to the edge coloring of graphs. Specifically, it states that for any simple graph \( G \), the chromatic index (the minimum number of colors needed to color the edges of the graph so that no two adjacent edges share the same color) is either equal to the maximum degree \( \Delta(G) \) of the graph or \( \Delta(G) + 1 \).