 
Summary: DOI: 10.1007/s004540032869x
Discrete Comput Geom 31:395403 (2004) Discrete & Computational
Geometry© 2004 SpringerVerlag New York Inc.
Decompositions and Connectivity of Matching
and Chessboard Complexes
Christos A. Athanasiadis
Department of Mathematics, University of Crete,
71409 Heraklion, Crete, Greece
caa@math.uoc.gr
Dedicated to Lou Billera on the occasion of his sixtieth birthday
Abstract. New lower bounds for the connectivity degree of the rhypergraph 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 Bjšorner et al. [5] are improved for r 3. Results on shellability of the chessboard
complex due to Ziegler [16] 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.
1. Introduction and Results
We first define the main objects of study in this paper. Given integers n r 2, the
rhypergraph matching complex Mn(r) is the simplicial complex on the vertex set Vn(r)
