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Self-similar Structure and Hamiltonicity

In: Hamiltonian Cycle Problem and Markov Chains

Author

Listed:
  • Vivek S. Borkar

    (IIT, Powai)

  • Vladimir Ejov

    (Flinders University)

  • Jerzy A. Filar

    (Flinders University)

  • Giang T. Nguyen

    (Université libre de Bruxelles)

Abstract

The class of cubic graphs provides a convenient “laboratory” for studying Hamiltonicity. This is because the Hamiltonian cycle problem is already NP-complete for this class and because there is freely available, reliable, software for enumerating all connected cubic graphs with N vertices (see, for example, Meringer [77]). This offers an opportunity to study the whole populations of these graphs with the goal of understanding the special nature of those members of that population that correspond to non-Hamiltonian graphs.

Suggested Citation

  • Vivek S. Borkar & Vladimir Ejov & Jerzy A. Filar & Giang T. Nguyen, 2012. "Self-similar Structure and Hamiltonicity," International Series in Operations Research & Management Science, in: Hamiltonian Cycle Problem and Markov Chains, edition 127, chapter 0, pages 163-178, Springer.
    • Handle: RePEc:spr:isochp:978-1-4614-3232-6_9
    DOI: 10.1007/978-1-4614-3232-6_9
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