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Let $P$ be a set of $n\geq 3$ points in general position in the plane. Theedge disjointness graph $D(P)$ of $P$ is the graph whose vertices are all theclosed straight line segments with endpoints in $P$, two of which are adjacentin $D(P)$ if and only if they are disjoint. We show that the connectivity of$D(P)$ is at least$\binom{\lfloor\frac{n-2}{2}\rfloor}{2}+\binom{\lceil\frac{n-2}{2}\rceil}{2}$,and that this bound is tight for each $n\geq 3$.

On the connectivity of the disjointness graph of segments of point sets in general position in the plane