### Abstract

Finding a Hamiltonian cycle in a graph is one of the classical NP-complete problems. Complexity of the Hamiltonian problem in permutation graphs has been a well-known open problem. In this paper the authors settle the complexity of the Hamiltonian problem in the more general class of cocomparability graphs. It is shown that the Hamiltonian cycle existence problem for cocomparability graphs is in P. A polynomial time algorithm for constructing a Hamiltonian path and cycle is also presented. The approach is based on exploiting the relationship between the Hamiltonian problem in a cocomparability graph and the bump number problem in a partial order corresponding to the transitive orientation of its complementary graph.

Original language | English (US) |
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Pages (from-to) | 520-552 |

Number of pages | 33 |

Journal | SIAM Journal on Computing |

Volume | 23 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 1994 |

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### ASJC Scopus subject areas

- Computer Science(all)
- Mathematics(all)

### Cite this

*SIAM Journal on Computing*,

*23*(3), 520-552. https://doi.org/10.1137/S0097539791200375

**Polynomial algorithms for Hamiltonian cycle in cocomparability graphs.** / Deogun, Jitender S.; Steiner, George.

Research output: Contribution to journal › Article

*SIAM Journal on Computing*, vol. 23, no. 3, pp. 520-552. https://doi.org/10.1137/S0097539791200375

}

TY - JOUR

T1 - Polynomial algorithms for Hamiltonian cycle in cocomparability graphs

AU - Deogun, Jitender S.

AU - Steiner, George

PY - 1994/1/1

Y1 - 1994/1/1

N2 - Finding a Hamiltonian cycle in a graph is one of the classical NP-complete problems. Complexity of the Hamiltonian problem in permutation graphs has been a well-known open problem. In this paper the authors settle the complexity of the Hamiltonian problem in the more general class of cocomparability graphs. It is shown that the Hamiltonian cycle existence problem for cocomparability graphs is in P. A polynomial time algorithm for constructing a Hamiltonian path and cycle is also presented. The approach is based on exploiting the relationship between the Hamiltonian problem in a cocomparability graph and the bump number problem in a partial order corresponding to the transitive orientation of its complementary graph.

AB - Finding a Hamiltonian cycle in a graph is one of the classical NP-complete problems. Complexity of the Hamiltonian problem in permutation graphs has been a well-known open problem. In this paper the authors settle the complexity of the Hamiltonian problem in the more general class of cocomparability graphs. It is shown that the Hamiltonian cycle existence problem for cocomparability graphs is in P. A polynomial time algorithm for constructing a Hamiltonian path and cycle is also presented. The approach is based on exploiting the relationship between the Hamiltonian problem in a cocomparability graph and the bump number problem in a partial order corresponding to the transitive orientation of its complementary graph.

UR - http://www.scopus.com/inward/record.url?scp=0028452825&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0028452825&partnerID=8YFLogxK

U2 - 10.1137/S0097539791200375

DO - 10.1137/S0097539791200375

M3 - Article

AN - SCOPUS:0028452825

VL - 23

SP - 520

EP - 552

JO - SIAM Journal on Computing

JF - SIAM Journal on Computing

SN - 0097-5397

IS - 3

ER -