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Crossing Numbers and Skewness of Some Generalized Petersen Graphs

  • G. L. Chia
  • C. L. Lee
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3330)

Abstract

The skewness of a graph G is the minimum number of edges in G whose removal results in a planar graph. In this paper, we show that the skewness of the generalized Petersen graph P (3k, k) is \(\lceil\frac{k}{2}+1\rceil\), where k ≥ 4. As a byproduct, it is shown that for k ≥ 4, \(\lceil\frac{k}{2}+1\rceil \leq cr(P(3k,k)) \leq k\), where cr (G) denotes the crossing number of G.

Keywords

Regular Graph Discrete Math Edge Incident Internal Vertex Pigeonhole Principle 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • G. L. Chia
    • 1
  • C. L. Lee
    • 1
  1. 1.Institute of Mathematical SciencesUniversity of MalayaKuala LumpurMalaysia

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