Nesting points in the sphere

  • Authors:

  • Dan Archdeacon;Feliu Sagols

  • Affiliations:

  • Dept. of Computer Science, Mathematics & Statistics, University of Vermont, 16 Colchester Avenue, Burlington, VT;Dept. of Computer Science, University of Vermont, Burlington

  • Venue:
  • Discrete Mathematics - Algebraic and topological methods in graph theory
  • Year:
  • 2002

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Abstract

Let G be a graph embedded in the sphere. A k-nest of a point x not in G is a collection C1,....,Ck of disjoint cycles such that for each Ci, the side containing x also contains Cj for each j i. An embedded graph is k-nested if each point not on the graph has a k-nest. In this paper we examine k-nested maps. We find the minor-minimal k-nested maps small values of k. In particular, we find the obstructions (under the minor order) for the class of planar maps with the property that one face's boundary meets all other face boundaries.