  The $k$-tuple domination problem, for a fixed positive integer $k$, is to
find a minimum sized vertex subset such that every vertex in the graph is
dominated by at least $k$ vertices in this set. The $k$-tuple domination is
NP-hard even for chordal graphs. For the class of circular-arc graphs, its
complexity remains open for $k\geq 2$. A $0,1$-matrix has the consecutive 0's
property (C0P) for columns if there is a permutation of its rows that places
the 0's consecutively in every column. Due to A. Tucker, graphs whose augmented
adjancency matrix has the C0P for columns are circular-arc. In this work we
study the $k$-tuple domination problem on graphs $G$ whose augmented adjacency
matrix has the C0P for columns, for $ 2\leq k\leq |U|+3$, where $U$ is the set
of universal vertices of $G$. From an algorithmic point of view, this takes
linear time.
