Simplicial Maps of Graphs That Factor Through an Arc
by
David J. Ryden
Tulane University

It is shown that a simplicial map \phi from a connected graph into a graph can be factored through an arc if and only if there are a monotone map \mu, a sequence \pi₁, \pi₂, ..., \pi_n of folds, and an irreducible map \psi whose domain is an arc such that \phi = \psi o \pi_n o ... o \pi₂ o \pi₁ o \mu.

Date received: March 1, 2002