Rainbow numbers for matchings and complete graphs
If \(H\) is a graph and \(n\) is a positive integer then the rainbow number \(\text{rb}(n,H)\) is defined as the minimum number of colours that must be used to colour the edges of \(K_n\) in such a way that the edges of a copy of \(H\) in \(K_n\) have pairwise different colours (such a copy of \(H\) is called rainbow or totally multicoloured). The rainbow numbers \(\text{rb}(n,K_k)\) for all \(n\geq k\geq 4\) and the rainbow numbers \(\text{rb}(n,k{K_2})\) for all \(k\geq 2\) and \(n\geq 3k+3\) are determined. A short overview of earlier results and a relationship to some results from extremal graph theory are presented as well.
scientific article; zbMATH DE number 2105623