Graphs that are images of reduced 2-to-1 maps
by
Van Nall
University of Richmond.

A reduced map is a continuous function between continua such that every proper subcontinuum of the range has disconnected preimage. We recently showed that a graph G is the image of a reduced k-to-1 map if and only if it does not contain a finite set B such that G \B has at least k|B| components. Such a set B is called a k-to-1 cut set. Here we give a constructive characterization in terms of graph decompositions for the k=2 case which among other things reduces the complexity of determining whether a graph has a 2-to-1 cut set. In the process we establish an interesting connection between reduced maps onto graphs and strongly connected digraphs.

Date received: February 15, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caca-41.