Arboricity and tree-packing in locally finite graphs

Authors:
Maya Jakobine Stein
Affiliations:
Mathematisches Seminar, Universität Hamburg, Bundesstraße 55, 20146 Hamburg, Germany
Venue:
Journal of Combinatorial Theory Series B
Year:
2006

Citing 5
Cited 0

On Infinite Cycles I

Combinatorica
On Infinite Cycles II

Combinatorica
Topological paths, cycles and spanning trees in infinite graphs

European Journal of Combinatorics - Special issue: Topological graph theory
The Cycle Space of an Infinite Graph

Combinatorics, Probability and Computing
On end degrees and infinite cycles in locally finite graphs

Combinatorica

Quantified Score

Hi-index	0.00

Visualization

Abstract

Nash-Williams' arboricity theorem states that a finite graph is the edge-disjoint union of at most k forests if no set of @? vertices induces more than k(@?-1) edges. We prove a natural topological extension of this for locally finite infinite graphs, in which the partitioning forests are acyclic in the stronger sense that their Freudenthal compactification-the space obtained by adding their ends-contains no homeomorphic image of S^1. The strengthening we prove, which requires an upper bound on the end degrees of the graph, confirms a conjecture of Diestel [The cycle space of an infinite graph, Combin. Probab. Comput. 14 (2005) 59-79]. We further prove for locally finite graphs a topological version of the tree-packing theorem of Nash-Williams and Tutte.