Constructions for Nonhamiltonian Burkard-Hammer Graphs

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


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.


Bipartite Graph Complete Graph Minimum Degree Hamilton Cycle Hamilton Path 
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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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