  A normal Helly circular-arc graph is the intersection graph of arcs on a
circle of which no three or less arcs cover the whole circle. Lin, Soulignac,
and Szwarcfiter [Discrete Appl. Math. 2013] characterized circular-arc graphs
that are not normal Helly circular-arc graphs, and used it to develop the first
recognition algorithm for this graph class. As open problems, they ask for the
forbidden induced subgraph characterization and a direct recognition algorithm
for normal Helly circular-arc graphs, both of which are resolved by the current
paper. Moreover, when the input is not a normal Helly circular-arc graph, our
recognition algorithm finds in linear time a minimal forbidden induced subgraph
as certificate.
