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Acta Informatica

, Volume 34, Issue 3, pp 231–243 | Cite as

Reduced constants for simple cycle graph separation

  • Hristo N. Djidjev
  • Shankar M. Venkatesan

Abstract.

 If G is an n vertex maximal planar graph and δ≤1 3, then the vertex set of G can be partitioned into three sets A, B, C such that neither A nor B contains more than (1−δ)n vertices, no edge from G connects a vertex in A to a vertex in B, and C is a cycle in G containing no more than (√2δ+√2−2δ)√n+O(1) vertices. Specifically, when δ=1 3, the separator C is of size (√2/3+√4/3)√n+O(1), which is roughly 1.97√n. The constant 1.97 is an improvement over the best known so far result of Miller 2√2≈2.82. If non-negative weights adding to at most 1 are associated with the vertices of G, then the vertex set of G can be partitioned into three sets A, B, C such that neither A nor B has weight exceeding 1−δ, no edge from G connects a vertex in A to a vertex in B, and C is a simple cycle with no more than 2√n+O(1) vertices.

Keywords

Planar Graph Simple Cycle Graph Separation Cycle Graph Maximal Planar Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Hristo N. Djidjev
    • 1
  • Shankar M. Venkatesan
    • 2
  1. 1.Department of Computer Science, Rice University, Houston, TX 77251, USAUS
  2. 2.Department of Computer Science, University of Minnesota, Minneapolis, MN 55455, USAUS

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