Equivariant collapses and the homotopy type of iterated clique graphs
نویسندگان
چکیده
منابع مشابه
Equivariant collapses and the homotopy type of iterated clique graphs
The clique graph K(G) of a simple graph G is the intersection graph of its maximal complete subgraphs, and we define iterated clique graphs by K(G) = G, K(G) = K(K(G)). We say that two graphs are homotopy equivalent if their simplicial complexes of complete subgraphs are so. From known results it can be easily inferred that Kn(G) is homotopy equivalent to G for every n if G belongs to the class...
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To any finite poset P we associate two graphs which we denote by Ω(P ) and 0(P ). Several standard constructions can be seen as Ω(P ) or 0(P ) for suitable posets P , including the comparability graph of a poset, the clique graph of a graph and the 1–skeleton of a simplicial complex. We interpret graphs and posets as simplicial complexes using complete subgraphs and chains as simplices. Then we...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2008
ISSN: 0012-365X
DOI: 10.1016/j.disc.2007.06.021