Independence complexes and incidence graphs

Authors

  • Shuichi Tsukuda University of the Ryukyus

DOI:

https://doi.org/10.11575/cdm.v12i1.62277

Keywords:

Poset, Graph, Independent set

Abstract

We show that the independence complex of the incidence graph of
a hypergraph is homotopy equivalent to the combinatorial Alexander dual of
the independence complex of the hypergraph, generalizing a result of Csorba.
As an application, we refine and generalize a result of Kawamura on a
relation between the homotopy types of the independence complex and
the edge covering complex of a graph.

References

Jonathan~Ariel Barmak.

Star clusters in independence complexes of graphs.

Adv. Math., 241:33--57, 2013.

Peter Csorba.

Subdivision yields Alexander duality on independence complexes.

Electron. J. Combin., 16(2, Special volume in honor of Anders Bjorner):Research Paper 11, 7, 2009.

Jakob Jonsson.

On the topology of independence complexes of triangle-free graphs.

preprint.

Kazuhiro Kawamura.

Independence complexes and edge covering complexes via Alexander duality.

Electron. J. Combin., 18(1):Paper 39, 6, 2011.

Uwe Nagel and Victor Reiner.

Betti numbers of monomial ideals and shifted skew shapes.

Electron. J. Combin., 16(2, Special volume in honor of Anders Bjorner):Research Paper 3, 59, 2009.

Daniel Quillen.

Homotopy properties of the poset of nontrivial {$p$}-subgroups of a group.

Adv. in Math., 28(2):101--128, 1978.

James~W. Walker.

Canonical homeomorphisms of posets.

European Journal of Combinatorics, 9(2):97--107, 1988.

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Published

2017-09-27

Issue

Vol. 12 No. 1 (2017)

Section

Articles

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