Titlebook: Simplicial Complexes of Graphs; Jakob Jonsson Book 2008 Springer-Verlag Berlin Heidelberg 2008 Graph.Homotopy.Hypergraph.Matching.Sim.Vert

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Acumen

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Graph PropertiesRecall from Chapter 1 that a monotone graph property is a simplicial complex of graphs — on a fixed vertex set . — that is invariant under the natural action of the symmetric group on .. Roughly speaking, the monotone graph properties to be examined in this book are of four kinds:

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Digraph PropertiesWe proceed with digraph complexes, which are complexes in which each 0—cell is an ordered - as opposed to unordered - pair. We still denote a pair (.) as ., but now . and . are different elements. We may divide the monotone digraph properties to be examined into two groups:

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Directed Variants of Forests and Bipartite GraphsWe consider complexes of directed variants of forests and bipartite graphs and some relatives thereof.