  A graph is concave-round if its vertices can be circularly enumerated so that
the closed neighbourhood of each vertex is an interval in the enumeration. In
this work, we give a minimal forbidden induced subgraph characterization for
the class of concave-round graphs, solving a problem posed by Bang-Jensen,
Huang, and Yeo [SIAM J Discrete Math, 13:179--193, 2000]. In addition, we show
that it is possible to find one such forbidden induced subgraph in linear time
in any given graph that is not concave-round. As part of the analysis, we
obtain characterizations by minimal forbidden submatrices for the circular-ones
property for rows and for the circular-ones property for rows and columns and
show that, also for both variants of the property, one of the corresponding
forbidden submatrices can be found (if present) in any given matrix in linear
time. We make some final remarks regarding connections to some classes of
circular-arc graphs.
