  The Erd\H{o}s--Faber--Lov\'{a}sz Conjecture, posed in 1972, states that if a
graph $G$ is the union of $n$ cliques of order $n$ (referred to as defining
$n$-cliques) such that two cliques can share at most one vertex, then the
vertices of $G$ can be properly coloured using $n$ colours. Although still open
after almost 50 years, it can be easily shown that the conjecture is true when
every shared vertex belongs to exactly two defining $n$-cliques. We here
provide a quick and easy algorithm to colour the vertices of $G$ in this case,
and discuss connections with clique-decompositions and edge-colourings of
graphs.
