Pseudo-hamiltonian graphs

  • Luitpold Babel
  • Gerhard J. Woeginger
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1335)


A pseudo-h-hamiltonian cycle in a graph is a closed walk that visits every vertex exactly h times. We present a variety of combinatorial and algorithmic results on pseudo- h-hamiltonian cycles: First, we show that deciding whether a graph is pseudo-h-hamiltonian is NP-complete for any given h ≥ 1. Surprisingly, deciding whether there exists an h ≥ 1 such that the graph is pseudo-h-hamiltonian, can be done in polynomial time. We also present sufficient conditions for pseudo- h-hamiltonicity that are based on stable sets and on toughness. Moreover, we investigate the computational complexity of finding pseudo-h-hamiltonian cycles on special graph classes like bipartite graphs, split graphs, planar graphs, cocomparability graphs; in doing this, we establish a precise separating line between easy and difficult cases of this problem.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Luitpold Babel
    • 1
  • Gerhard J. Woeginger
    • 2
  1. 1.Institut für MathematikTU MünchenMünchenGermany
  2. 2.Institut für Mathematik BTU GrazGrazAustria

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