  Let $P$ be a set of $n\geq 2$ points in general position in $R^2$. The edge
disjointness graph $D(P)$ of $P$ is the graph whose vertices are all the closed
straight line segments with endpoints in $P$, two of which are adjacent in
$D(P)$ if and only if they are disjoint. In this note, we give a full
characterization of all those edge disjointness graphs that are hamiltonian.
More precisely, we shall show that (up to order type isomorphism) there are
exactly 8 instances of P for which $D(P)$ is not hamiltonian. Additionally,
from one of these 8 instances, we derive a counterexample to a criterion for
the existence of hamiltonian cycles due to A. D. Plotnikov in 1998.
