On the smallest sets blocking simple perfect matchings in a convex geometric graph

Abstract

In this paper we present a complete characterization of the smallest sets which block all the simple perfect matchings in a complete convex geometric graph on $2m$ vertices. In particular, we show that all these sets are caterpillar graphs with a special structure, and that their total number is $m\cdot 2^{m-1}$.

15 pages, 8 figures