# Wan, Peng-Jun

## Coloring squares of hypercubes ★★

Author(s): Wan

If $G$ is a simple graph, we let $G^{(2)}$ denote the simple graph with vertex set $V(G)$ and two vertices adjacent if they are distance $\le 2$ in $G$.

\begin{conjecture} $\chi(Q_d^{(2)}) = 2^{ \lfloor \log_2 d \rfloor + 1}$. \end{conjecture}

Keywords: coloring; hypercube