Geodesic
Subdivision yields Alexander duality on independence complexes
The electronic journal of combinatorics, The Björner Festschrift volume, Tome 16 (2009) no. 2
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We study how the homotopy type of the independence complex of a graph changes if we subdivide edges. We show that the independence complex becomes the Alexander dual if we place one new vertex on each edge of a graph. If we place two new vertices on each edge then the independence complex is the wedge of two spheres. Placing three new vertices on an edge yields the suspension of the independence complex.
DOI : 10.37236/77
Classification : 05C69, 55P10 
@article{10_37236_77,
     author = {P\'eter Csorba},
     title = {Subdivision yields {Alexander} duality on independence complexes},
     journal = {The electronic journal of combinatorics},
     year = {2009},
     volume = {16},
     number = {2},
     doi = {10.37236/77},
     zbl = {1171.05384},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/77/}
}
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Péter Csorba. Subdivision yields Alexander duality on independence complexes. The electronic journal of combinatorics, The Björner Festschrift volume, Tome 16 (2009) no. 2. doi: 10.37236/77

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