This book focuses on families of graphs on a fixed vertex set. We are particularly interested in graph complexes, which are graph families closed under deletion of edges. Equivalently, a graph complex Α has the property that if G ∈ Α and e is an edge in G, then the graph obtained from G 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 may realize Α as a geometric object and hence analyze its topology. Indeed, this is the main purpose of the book.
Keywords
- Bipartite Graph
- Simplicial Complex
- Vertex Cover
- Homotopy Type
- Graph Property
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
(2008). Introduction and Overview. In: Simplicial Complexes of Graphs. Lecture Notes in Mathematics, vol 1928. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75859-4_1
Download citation
DOI: https://doi.org/10.1007/978-3-540-75859-4_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-75858-7
Online ISBN: 978-3-540-75859-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)
