Between ends and fibers

Let Γ be an infinite, locally finite, connected graph with distance function δ. Given a ray P in Γ and a constant C ≥ 1, a vertex-sequence {xn}∞ n=0 ⊆ V P is said to be regulated by C if, for all n ∈ N, xn+1 never precedes xn on P, each vertex of P appears at most C times in the sequence, and δP (xn, xn+1) ≤ C. 1 

• Type: Journal
• Year: 2007
• Where: JGT
• Authors: C. Paul Bonnington, R. Bruce Richter, Mark E. Watkins
• Keywords: Distance Function, JGT 2007