Shellable graphs and sequentially Cohen-Macaulay bipartite graphs

@article{Tuyl2008ShellableGA,
  title={Shellable graphs and sequentially Cohen-Macaulay bipartite graphs},
  author={Adam Van Tuyl and Rafael H. Villarreal},
  journal={J. Comb. Theory, Ser. A},
  year={2008},
  volume={115},
  pages={799-814}
}
Associated to a simple undirected graph G is a simplicial complex ∆G whose faces correspond to the independent sets of G. We call a graph G shellable if ∆G is a shellable simplicial complex in the non-pure sense of Björner-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… CONTINUE READING
Highly Cited
This paper has 34 citations. REVIEW CITATIONS

From This Paper

Topics from this paper.

References

Publications referenced by this paper.
Showing 1-10 of 23 references

Distributive lattices

  • J. Herzog, T. Hibi
  • bipartite graphs and Alexander duality, J…
  • 2005
Highly Influential
10 Excerpts

Simplicial trees are sequentially Cohen-Macaulay

  • S. Faridi
  • J. Pure Appl. Algebra 190
  • 2003
Highly Influential
7 Excerpts

Cohen-Macaulay bipartite graphs

  • M. Estrada, R. H. Villarreal
  • Arch. Math. 68
  • 1997
Highly Influential
5 Excerpts

Combinatorics and Commutative Algebra

  • R. P. Stanley
  • Second edition. Progress in Mathematics 41. Birkh…
  • 1996
Highly Influential
6 Excerpts

Monomial ideals

  • H. T. Hà, A. Van Tuyl
  • edge ideals of hypergraphs, and their minimal…
  • 2006
1 Excerpt

Unmixed bipartite graphs

  • R. H. Villarreal
  • 2006
2 Excerpts

Similar Papers

Loading similar papers…