Locally finite graphs with ends: A topological approach. I: Basic theory

DOI10.1016/j.disc.2010.05.023zbMath1223.05198OpenAlexW2036888349MaRDI QIDQ2275376

Reinhard Diestel

Publication date: 8 August 2011

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2010.05.023

zbMATH Keywords

topologyinfinite graphboundaryendlocally finite graphfreudenthal compactification

Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10) Relations of low-dimensional topology with graph theory (57M15) Infinite graphs (05C63)

Related Items (16)

One-dimensional Peano continua with zero-dimensional wild part ⋮ Two-ended quasi-transitive graphs ⋮ Cycles through all finite vertex sets in infinite graphs ⋮ Labeled trees generating complete, compact, and discrete ultrametric spaces ⋮ A note on classes of subgraphs of locally finite graphs ⋮ Hamiltonian decompositions of 4‐regular Cayley graphs of infinite abelian groups ⋮ The Lovász-Cherkassky theorem for locally finite graphs with ends ⋮ Universal end-compactifications of locally finite graphs ⋮ Cycle decompositions: from graphs to continua ⋮ Locally finite graphs with ends: a topological approach. III. Fundamental group and homology ⋮ Algebraic flow theory of infinite graphs ⋮ Hamilton circles in Cayley graphs ⋮ On graph-like continua of finite length ⋮ Locally finite graphs with ends: A topological approach. II: Applications ⋮ Non-reconstructible locally finite graphs ⋮ Self-embeddings of trees

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Axioms for infinite matroids
• Bases and closures under infinite sums
• On infinite cycles. I, II
• Eulerian edge sets in locally finite graphs
• Locally finite graphs with ends: a topological approach. III. Fundamental group and homology
• The cycle space of a 3-connected locally finite graph is generated by its finite and infinite peripheral circuits
• Locally finite graphs with ends: A topological approach. II: Applications
• End spaces and spanning trees
• End spaces of graphs are normal
• Connected but not path-connected subspaces of infinite graphs
• Bicycles and left-right tours in locally finite graphs
• Topological circles and Euler tours in locally finite graphs
• Planarity and duality of finite and infinite graphs
• Géométrie et théorie des groupes. Les groupes hyperboliques de Gromov. (Geometry and group theory. The hyperbolic groups of Gromov)
• Infinite graphs and bicircular matroids
• Edge-ends in countable graphs
• Topological paths, cycles and spanning trees in infinite graphs
• Graph topologies induced by edge lengths
• Geodetic topological cycles in locally finite graphs
• On end degrees and infinite cycles in locally finite graphs
• Infinite Hamilton cycles in squares of locally finite graphs
• Normal Spanning Trees, Aronszajn Trees and Excluded Minors
• Duality in Infinite Graphs
• Duality of Ends
• Cycle spaces in topological spaces
• The bond and cycle spaces of an infinite graph
• Algebraic Potential Theory on Graphs
• The Cycle Space of an Infinite Graph
• Matroids and duality
• Equicardinality of Bases in B-Matroids
• Sur la Dualite en Theorie des Matroides
• Cycle‐cocycle partitions and faithful cycle covers for locally finite graphs
• Infinite Matroids

This page was built for publication: Locally finite graphs with ends: A topological approach. I: Basic theory