 
Summary: Nesting points in the sphere
Dan Archdeacon
Dept. of Computer Science
University of Vermont
Burlington, VT, USA 05405
email: dan.archdeacon@uvm.edu
Feliu Sagols
Dept. of Computer Science
University of Vermont
Burlington, VT, USA 05405
email: fsagols@emba.uvm.edu 1
July 26, 1999 (revised June 14, 2000)
Abstract
Let G be a graph embedded in the sphere. A knest of a point x
not in G is a collection C 1 ; : : : ; C k
of disjoint cycles such that for each
C i , the side containing x also contains C j for each j < i. An embedded
graph is knested if each point not on the graph has a knest. In this
paper we examine knested maps. We nd the minorminimal knested
maps small values of k. In particular, we nd the obstructions (under
