Achromatic index of \(K_{12}\). (English) Zbl 0933.05048

Horňák, Mirko

Ars Comb. 45, 271-275 (1997).

The achromatic index of a graph \(G\) is the maximum integer \(k\) such that there exists a proper colouring of the edges (i.e. in which no two adjacent edges have the same colour) in which each pair of colours appear on some pair of adjacent edges. The achromatic index of the complete graph \(K_n\) with \(n\) vertices is denoted by \(A(n)\). It is proved that \(A(12)=32\).

Reviewer: B.Zelinka (Liberec)

MSC:

05C15

Coloring of graphs and hypergraphs

Keywords:

achromatic index; edge colouring; complete graph