Anti-Ramsey numbers in complete \(k\)-partite graphs
Summary: The anti-Ramsey number \(AR\left( G, H\right)\) is the maximum number of colors in an edge-coloring of \(G\) such that \(G\) contains no rainbow subgraphs isomorphic to \(H\). In this paper, we discuss the anti-Ramsey numbers \(AR\left( K_{p_1, p_2, \ldots, p_k}, \mathcal{T}_n\right)\), \(AR\left( K_{p_1, p_2, \ldots, p_k}, \mathcal{M}\right)\), and \(AR\left( K_{p_1, p_2, \ldots, p_k}, \mathcal{C}\right)\) of \(K_{p_1, p_2, \ldots, p_k} \), where \(\mathcal{T}_n\), \(\mathcal{M}\), and \(\mathcal{C}\) denote the family of all spanning trees, the family of all perfect matchings, and the family of all Hamilton cycles in \(K_{p_1, p_2, \ldots, p_k}\), respectively.
scientific article; zbMATH DE number 7259943
scientific article