Introduction and Overview

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.