Hypercube-Anti-Ramsey Numbers of \(Q_5\)

Abstract

A rainbow coloring of the edges of a graph is a coloring such
that no two edges of the graph have the same color. The
anti-Ramsey number \(f(G, H)\) is the maximum number of colors
such that there is an \(H\)-anti-Ramsey edge coloring of \(G\), that is,
there exists no rainbow copy of the subgraph \(H\) of \(G\) in some
coloring of the edges of the host graph \(G\) with \(f(G, H)\) colors.

In this note, we exactly determine \(f(Q_5, Q_2)\) and \(f(Q_5, Q_3)\),
where \(Q_n\) is the \(n\)-dimensional hypercube.