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2008•arXiv (Cornell University)Open access

NP-Completeness of Hamiltonian Cycle Problem on Rooted Directed Path Graphs

B. S. Panda, Dinabandhu Pradhan

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Abstract

The Hamiltonian cycle problem is to decide whether a given graph has a Hamiltonian cycle. Bertossi and Bonuccelli (1986, Information Processing Letters, 23, 195-200) proved that the Hamiltonian Cycle Problem is NP-Complete even for undirected path graphs and left the Hamiltonian cycle problem open for directed path graphs. Narasimhan (1989, Information Processing Letters, 32, 167-170) proved that the Hamiltonian Cycle Problem is NP-Complete even for directed path graphs and left the Hamiltonian cycle problem open for rooted directed path graphs. In this paper we resolve this open problem by proving that the Hamiltonian Cycle Problem is also NP-Complete for rooted directed path graphs.

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The Hamiltonian cycle problem is to decide whether a given graph has a Hamiltonian cycle. Bertossi and Bonuccelli (1986, Information Processing Letters, 23, 195-200) proved that the Hamiltonian Cycle Problem is NP-Complete even for undirected path graphs and left the Hamiltonian cycle problem open for directed path graphs. Narasimhan (1989, Information Processing Letters, 32, 167-170) proved that the Hamiltonian Cycle Problem is NP-Complete even for directed path graphs and left the Hamiltonian cycle problem open for rooted directed path graphs. In this paper we resolve this open problem by proving that the Hamiltonian Cycle Problem is also NP-Complete for rooted directed path graphs.

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Available abstract

The Hamiltonian cycle problem is to decide whether a given graph has a Hamiltonian cycle. Bertossi and Bonuccelli (1986, Information Processing Letters, 23, 195-200) proved that the Hamiltonian Cycle Problem is NP-Complete even for undirected path graphs and left the Hamiltonian cycle problem open for directed path graphs. Narasimhan (1989, Information Processing Letters, 32, 167-170) proved that the Hamiltonian Cycle Problem is NP-Complete even for directed path graphs and left the Hamiltonian cycle problem open for rooted directed path graphs. In this paper we resolve this open problem by proving that the Hamiltonian Cycle Problem is also NP-Complete for rooted directed path graphs.

Key concepts: Hamiltonian path, Hamiltonian path problem, Longest path problem, Mathematics, Hamiltonian (control theory), Combinatorics, Indifference graph, Discrete mathematics

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