Note: Hamiltonian index is NP-complete

  • Authors:

  • Zdenk RyjáčEk;Gerhard J. Woeginger;Liming Xiong

  • Affiliations:

  • Department of Mathematics, University of West Bohemia, P.O. Box 314, 306 14 Pilsen, Czech Republic and Institute of Theoretical Computer Science (ITI), Charles University, P.O. Box 314, 306 14 Pil ...;Department of Math. and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands;Department of Mathematics, Beijing Institute of Technology, Beijing, 100081, PR China and Department of Mathematics, Qinghai University for Nationalities, PR China and Department of Mathematics, J ...

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2011

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Abstract

In this paper we show that the problem to decide whether the hamiltonian index of a given graph is less than or equal to a given constant is NP-complete (although this was conjectured to be polynomial). Consequently, the corresponding problem to determine the hamiltonian index of a given graph is NP-hard. Finally, we show that some known upper and lower bounds on the hamiltonian index can be computed in polynomial time.