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Constructions for Nonhamiltonian Burkard-Hammer Graphs

  • Ngo Dac Tan
  • Chawalit Iamjaroen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3330)

Abstract

A graph G = (V,E) is called a split graph if there exists a partition V = IK such that the subgraphs G[I ] and G[K] of G induced by I and K are empty and complete graphs, respectively. In 1980, Burkard and Hammer gave a necessary condition for split graphs with |I |<|K| to be hamiltonian. This condition is not sufficient. In this paper, we give two constructions for producing infinite families of split graphs with |I |<|K|, which satisfy the Burkard-Hammer condition but have no Hamilton cycles.

Keywords

Bipartite Graph Complete Graph Minimum Degree Hamilton Cycle Hamilton Path 
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 2005

Authors and Affiliations

  • Ngo Dac Tan
    • 1
    • 2
  • Chawalit Iamjaroen
    • 2
  1. 1.Institute of MathematicsHanoiVietnam
  2. 2.Department of MathematicsMahasarakham UniversityMahasarakhamThailand

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