  The connectivity of graphs of simplicial and polytopal complexes is a
classical subject going back at least to Steinitz, and the topic has since been
studied by many authors, including Balinski, Barnette, Athanasiadis and
Bjorner. In this note, we provide a unifying approach which allows us to obtain
more general results. Moreover, we provide a relation to commutative algebra by
relating connectivity problems to graded Betti numbers of the associated
Stanley--Reisner rings.
