Geodesic
Independence complexes and edge covering complexes via Alexander duality
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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The combinatorial Alexander dual of the independence complex $\mathrm{Ind}(G)$ and that of the edge covering complex $\mathrm{EC}(G)$ are shown to have isomorphic homology groups for each non-null graph $G$. This yields isomorphisms of homology groups of $\mathrm{Ind}(G)$ and $\mathrm{EC}(G)$ with homology dimensions being appropriately shifted and restricted. The results exhibits the complementary nature of homology groups of $\mathrm{Ind}(G)$ and $\mathrm{EC}(G)$ which had been proved by Ehrenborg-Hetyei, Engström, and Marietti-Testa for forests at homotopy level.
DOI : 10.37236/526
Classification : 05C10, 55P10, 05C05, 05C69, 05C99
Mots-clés : independence complex Ind(G) 
@article{10_37236_526,
     author = {Kazuhiro Kawamura},
     title = {Independence complexes and edge covering complexes via {Alexander} duality},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/526},
     zbl = {1229.05093},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/526/}
}
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Kazuhiro Kawamura. Independence complexes and edge covering complexes via Alexander duality. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/526

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