Decompositions and Connectivity of Matching and Chessboard Complexes

New lower bounds for the connectivity degree of the r-hypergraph matching and chessboard complexes are established by showing that certain skeleta of such complexes are vertex decomposable, in the sense of Provan and Billera, and hence shellable. The bounds given by Björner et al. are improved for r \ge 3. Results on shellability of the chessboard complex due to Ziegler are reproven in the case r=2 and an affirmative answer to a question raised recently by Wachs for the matching complex follows. The new bounds are conjectured to be sharp.