Pseudo-hamiltonian graphs

  • Luitpold Babel
  • Gerhard J. Woeginger


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 axe 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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How to Cite
Babel, L., & Woeginger, G. J. (2000). Pseudo-hamiltonian graphs. Acta Cybernetica, 14(4), 553-567. Retrieved from
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