Arboricity and tree-packing in locally finite graphs

12Citations
Citations of this article
4Readers
Mendeley users who have this article in their library.
Get full text

Abstract

Nash-Williams' arboricity theorem states that a finite graph is the edge-disjoint union of at most k forests if no set of ℓ vertices induces more than k(ℓ - 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 S1. 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. © 2005 Elsevier Inc. All rights reserved.

Cite

CITATION STYLE

APA

Stein, M. J. (2006). Arboricity and tree-packing in locally finite graphs. Journal of Combinatorial Theory. Series B, 96(2), 302–312. https://doi.org/10.1016/j.jctb.2005.08.003

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free