Blockers for Simple Hamiltonian Paths in Convex Geometric Graphs of Even Order

Let G be a complete convex geometric graph on 2m vertices, and let F be a family of subgraphs of G. A blocker for F is a set of edges, of smallest possible size, that meets every element of F. In Keller and Perles (Israel J Math 187:465–484, 2012) we gave an explicit description of all blockers for the family of simple perfect matchings (SPMs) of G. In this paper we show that the family of simple Hamiltonian paths in G has exactly the same blockers as the family of SPMs. Our argument is rather short, and provides a much simpler proof of the result of Keller and Perles (2012).