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.