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

SPER

Noncrossing GraphsRecall that the associahedron A. is the complex of graphs on the vertex set [.] without crossings and boundary edges. The associahedron was introduced by Stasheff [136]. We discuss the associahedron and some related dihedral properties, all defined in terms of crossing avoidance.

Minikin

Disconnected GraphsWe examine the complex NC. of disconnected graphs on . vertices. We also consider subcomplexes consisting of graphs with certain restrictions on the vertex size of the connected components.

白杨

Jakob JonssonIncludes supplementary material:

Agronomy

演讲

congenial

Book 2008, including commutative algebra, geometry, and knot theory. Identifying each graph with its edge set, one may view a graph complex as a simplicial complex and hence interpret it as a geometric object. This volume examines topological properties of graph complexes, focusing on homotopy type and homol

opinionated

Introduction and Overviewedges. Equivalently, a graph complex Α has the property that if . ∈ Α and . is an edge in ., then the graph obtained from . by removing e is also in Α. Since the vertex set is fixed, we may identify each graph in Α with its edge set and hence interpret Α as a simplicial complex. In particular, we ma

巫婆

Abstract Graphs and Set Systemsgraphs, and hypergraphs. Section 2.2 is devoted to posets and lattices. We proceed with abstract simplicial complexes in Section 2.3 and conclude the chapter with some matroid theory in Section 2.4 and a few words about integer partitions in Section 2.5.

弯弯曲曲

Discrete Morse Theory has proven to be a powerful tool for analyzing the topology of a wide range of different complexes [4, 32, 36, 60, 94, 95, 118]. For an interesting application of discrete Morse theory to geometry, see Crowley [34].

仔细检查

Miscellaneous Resultstion 6.2 contains a discussion about the concept of depth, whereas Section 6.3 deals with the related concept of vertex-decomposability. In Section 6.4 at the end of the chapter, we present a few simple enumerative results.