Arboricity and tree-packing in locally finite graphs

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

• Type: Journal
• Year: 2006
• Where: JCT
• Authors: Maya Jakobine Stein
• Keywords: Edge-disjoint Union, Finite Graph, JCT 2006, Natural Topological Extension