  The satisfiability problem is NP-complete but there are subclasses where all
the instances are satisfiable. For this, restrictions on the shape of the
formula are made. Darman and D\"ocker show that the subclass MONOTONE
$3$-SAT-($k$,1) with $k \geq 5$ proves to be NP-complete and pose the open
question whether instances of MONOTONE $3$-SAT-(3,1) are satisfiable. This
paper shows that all instances of MONOTONE $3$-SAT-(3,1) are satisfiable using
the new concept of a color-structures.
