It is an odd definition of concave. It would make more sense to me to require that the line joining two points on the state's border does not cross in and out o

It is an odd definition of concave. It would make more sense to me to require that the line joining two points on the state's border does not cross in and out of the original state when determining the number of other states it crosses... This doesn't really capture concave as a geometric concept either but more aligned with the idea that it is a local property.