  Let $H$ be an edge-weighted graph, and let $G$ be a subgraph of $H$. We say
that $G$ is an $f$-fault-tolerant $t$-spanner for $H$, if the following is true
for any subset $F$ of at most $f$ edges of $G$: For any two vertices $p$ and
$q$, the shortest-path distance between $p$ and $q$ in the graph $G \setminus
F$ is at most $t$ times the shortest-path distance between $p$ and $q$ in the
graph $H \setminus F$.
  Recently, Bodwin, Haeupler, and Parter generalized this notion to the case
when $F$ can be any set of edges in $G$, as long as the maximum degree of $F$
is at most $f$. They gave constructions for general graphs $H$.
  We first consider the case when $H$ is a complete graph whose vertex set is
an arbitrary metric space. We show that if this metric space contains a
$t$-spanner with $m$ edges, then it also contains a graph $G$ with $O(fm)$
edges, that is resilient to edge faults of maximum degree $f$ and has stretch
factor $O(ft)$.
  Next, we consider the case when $H$ is a complete graph whose vertex set is a
metric space that admits a well-separated pair decomposition. We show that, if
the metric space has such a decomposition of size $m$, then it contains a graph
with at most $(2f+1)^2 m$ edges, that is resilient to edge faults of maximum
degree $f$ and has stretch factor at most $1+\varepsilon$, for any given
$\varepsilon > 0$. For example, if the vertex set is a set of $n$ points in
$\mathbb{R}^d$ ($d$ being a constant) or a set of $n$ points in a metric space
of bounded doubling dimension, then the spanner has $O(f^2 n)$ edges.
  Finally, for the case when $H$ is a complete graph on $n$ points in
$\mathbb{R}^d$, we show how natural variants of the Yao- and $\Theta$-graphs
lead to graphs with $O(fn)$ edges, that are resilient to edge faults of maximum
degree $f$ and have stretch factor at most $1+\varepsilon$, for any given
$\varepsilon > 0$.
