  A geometric $t$-spanner on a set of points in Euclidean space is a graph
containing for every pair of points a path of length at most $t$ times the
Euclidean distance between the points. Informally, a spanner is
$\mathcal{O}(k)$-robust if deleting $k$ vertices only harms $\mathcal{O}(k)$
other vertices. We show that on any one-dimensional set of $n$ points, for any
$\varepsilon>0$, there exists an $\mathcal{O}(k)$-robust $1$-spanner with
$\mathcal{O}(n^{1+\varepsilon})$ edges. Previously it was only known that
$\mathcal{O}(k)$-robust spanners with $\mathcal{O}(n^2)$ edges exists and that
there are point sets on which any $\mathcal{O}(k)$-robust spanner has
$\Omega(n\log{n})$ edges.
