Complexity of Hamiltonian Cycle Reconfiguration
Department of Information Systems Creation, Faculty of Engineering, Kanagawa University, Rokkakubashi 3-27-1 Kanagawa-ku, Yokohama-shi, Kanagawa 221-8686, Japan
Received: 25 February 2018 / Revised: 17 August 2018 / Accepted: 14 September 2018 / Published: 17 September 2018
The Hamiltonian cycle reconfiguration problem asks, given two Hamiltonian cycles
of a graph G
, whether there is a sequence of Hamiltonian cycles
can be obtained from
by a switch for each i
, where a switch is the replacement of a pair of edges
on a Hamiltonian cycle with the edges
, given that
did not appear on the cycle. We show that the Hamiltonian cycle reconfiguration problem is PSPACE-complete, settling an open question posed by Ito et al. (2011) and van den Heuvel (2013). More precisely, we show that the Hamiltonian cycle reconfiguration problem is PSPACE-complete for chordal bipartite graphs, strongly chordal split graphs, and bipartite graphs with maximum degree 6. Bipartite permutation graphs form a proper subclass of chordal bipartite graphs, and unit interval graphs form a proper subclass of strongly chordal graphs. On the positive side, we show that, for any two Hamiltonian cycles of a bipartite permutation graph and a unit interval graph, there is a sequence of switches transforming one cycle to the other, and such a sequence can be obtained in linear time.
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MDPI and ACS Style
Takaoka, A. Complexity of Hamiltonian Cycle Reconfiguration. Algorithms 2018, 11, 140.
Takaoka A. Complexity of Hamiltonian Cycle Reconfiguration. Algorithms. 2018; 11(9):140.
Takaoka, Asahi. 2018. "Complexity of Hamiltonian Cycle Reconfiguration." Algorithms 11, no. 9: 140.
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