Proofs of Theorems

We will adopt the following notational conventions. “w.l.g.” abbreviates “without loss of generality”, “r.h.s.” abbreviates “right hand side”, and “l.h.s.” abbreviates “left hand side”. Any sum over the empty set is equal to 0 and any product over the empty set is 1. R(I,J) represents a directed path from I to J. If U is an undirected path from A to B, and X and Y occur on U, then we will denote the subpath of U between X to Y as U(X,Y). T(I,J) represents a trek in T(I,J). The definitions of all technical terms in this chapter that have not been defined in Chapters 2 or 3 have been placed in a glossary following the chapter.