Anti-Ramsey Numbers of Small Graphs

Abstract

The anti-Ramsey number \(AR(n,G)\), for a graph \(G\) and an integer \(n \geq |V(G)|\), is defined to be the minimal integer \(r\) such that in any edge-colouring of \(K_n\) by at least \(r\) colours there is a multicoloured copy of \(G\), namely, a copy of \(G\) whose edges have distinct colours. In this paper, we determine the anti-Ramsey numbers of all graphs having at most four edges.