  We consider the localization game played on graphs, wherein a set of cops
attempt to determine the exact location of an invisible robber by exploiting
distance probes. The corresponding optimization parameter for a graph $G$ is
called the localization number and is written $\zeta (G)$. We settle a
conjecture of \cite{nisse1} by providing an upper bound on the localization
number as a function of the chromatic number. In particular, we show that every
graph with $\zeta (G) \le k$ has degeneracy less than $3^k$ and, consequently,
satisfies $\chi(G) \le 3^{\zeta (G)}$. We show further that this degeneracy
bound is tight. We also prove that the localization number is at most 2 in
outerplanar graphs, and we determine, up to an additive constant, the
localization number of hypercubes.
