The homology of a locally finite graph with ends

We show that the topological cycle space of a locally finite graph is a canonical quotient of the first singular homology group of its Freudenthal compactification, and we characterize the graphs for which the two coincide. We construct a new singular-type homology for non-compact spaces with ends, which in dimension 1 captures precisely the topological cycle space of graphs but works in any dimension.

• Type: Journal
• Year: 2010
• Where: COMBINATORICA
• Authors: Reinhard Diestel, Philipp Sprüssel
• Keywords: COMBINATORICA 2010, Freudenthal Compactification, Machine Learning, Singular Homology Group, Topological Cycle Space