On the Erdős–Simonovits–Sós Conjecture about the Anti-Ramsey Number of a Cycle

Source abstract

Given a positive integer n and a family of graphs, let denote the maximum number of colours in an edge-colouring of such that no subgraph of belonging to has distinct colours on its edges. Erdös, Simonovits and Sós [6] conjectured for fixed k with that . This has been proved for . For general k , in this paper we improve the previous bound of to . For even k , we further improve it to . We also prove that , which is sharp.