Colouring, stable sets and perfect graphs
Handbook of combinatorics (vol. 1)
Dirac's theorem on chordal graphs and Alexander duality
European Journal of Combinatorics
Distributive Lattices, Bipartite Graphs and Alexander Duality
Journal of Algebraic Combinatorics: An International Journal
Journal of Combinatorial Theory Series A
Whiskers and sequentially Cohen--Macaulay graphs
Journal of Combinatorial Theory Series A
Erdős-Ko-Rado theorems for simplicial complexes
Journal of Combinatorial Theory Series A
Splittings of independence complexes and the powers of cycles
Journal of Combinatorial Theory Series A
Algorithmic complexity of finding cross-cycles in flag complexes
Proceedings of the twenty-eighth annual symposium on Computational geometry
On the structure of the h-vector of a paving matroid
European Journal of Combinatorics
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Associated to a simple undirected graph G is a simplicial complex @D"G whose faces correspond to the independent sets of G. We call a graph G shellable if @D"G is a shellable simplicial complex in the non-pure sense of Bjorner-Wachs. We are then interested in determining what families of graphs have the property that G is shellable. We show that all chordal graphs are shellable. Furthermore, we classify all the shellable bipartite graphs; they are precisely the sequentially Cohen-Macaulay bipartite graphs. We also give a recursive procedure to verify if a bipartite graph is shellable. Because shellable implies that the associated Stanley-Reisner ring is sequentially Cohen-Macaulay, our results complement and extend recent work on the problem of determining when the edge ideal of a graph is (sequentially) Cohen-Macaulay. We also give a new proof for a result of Faridi on the sequentially Cohen-Macaulayness of simplicial forests.