Connectivity of pseudomanifold graphs from an algebraic point of view
  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. 
Karim A. Adiprasito, Afshin Goodarzi and Matteo Varbaro
math.CO math.AC