Hamiltonian paths in some classes of grid graphs.

*(English)*Zbl 1245.05081Summary: The Hamiltonian path problem for general grid graphs is known to be NP-complete. In this paper, we give necessary and sufficient conditions for the existence of Hamiltonian paths in \(L\)-alphabet, \(C\)-alphabet, \(F\)-alphabet, and \(E\)-alphabet grid graphs. We also present linear-time algorithms for finding Hamiltonian paths in these graphs.

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\textit{F. Keshavarz-Kohjerdi} and \textit{A. Bagheri}, J. Appl. Math. 2012, Article ID 475087, 17 p. (2012; Zbl 1245.05081)

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##### References:

[1] | R. Diestel, Graph Theory, vol. 173, Springer, New York, NY, USA, 2nd edition, 2000. · Zbl 0974.46031 |

[2] | M. R. Garey and D. S. Johnson, Computers and Intractability, W. H. Freeman and Co., San Francisco, Calif, USA, 1979. · Zbl 0411.68039 |

[3] | P. Damaschke, “Paths in interval graphs and circular arc graphs,” Discrete Mathematics, vol. 112, no. 1-3, pp. 49-64, 1993. · Zbl 0777.05081 |

[4] | L. Du, “A polynomial time algorithm for hamiltonian cycle (Path),” in Proceedings of the International MultiConference of Engineers and Computer Scientists (IMECS ’10), vol. 1, pp. 17-19, Hong Kong, 2010. |

[5] | R. J. Gould, “Advances on the Hamiltonian problem-a survey,” Graphs and Combinatorics, vol. 19, no. 1, pp. 7-52, 2003. · Zbl 1024.05057 |

[6] | Y. Gurevich and S. Shelah, “Expected computation time for Hamiltonian path problem,” SIAM Journal on Computing, vol. 16, no. 3, pp. 486-502, 1987. · Zbl 0654.68083 |

[7] | S.-S. Kao and L.-H. Hsu, “Spider web networks: a family of optimal, fault tolerant, Hamiltonian bipartite graphs,” Applied Mathematics and Computation, vol. 160, no. 1, pp. 269-282, 2005. · Zbl 1057.05052 |

[8] | M. S. Rahman and M. Kaykobad, “On Hamiltonian cycles and Hamiltonian paths,” Information Processing Letters, vol. 94, no. 1, pp. 37-41, 2005. · Zbl 1182.68142 |

[9] | F. Luccio and C. Mugnia, “Hamiltonian paths on a rectangular chessboard,” in Proceedings of the 16th Annual Allerton Conference, pp. 161-173, 1978. |

[10] | A. Itai, C. H. Papadimitriou, and J. L. Szwarcfiter, “Hamilton paths in grid graphs,” SIAM Journal on Computing, vol. 11, no. 4, pp. 676-686, 1982. · Zbl 0506.05043 |

[11] | C. Zamfirescu and T. Zamfirescu, “Hamiltonian properties of grid graphs,” SIAM Journal on Discrete Mathematics, vol. 5, no. 4, pp. 564-570, 1992. · Zbl 0770.05073 |

[12] | S. D. Chen, H. Shen, and R. Topor, “An efficient algorithm for constructing Hamiltonian paths in meshes,” Parallel Computing. Theory and Applications, vol. 28, no. 9, pp. 1293-1305, 2002. · Zbl 0999.68253 |

[13] | W. Lenhart and C. Umans, “Hamiltonian cycles in solid grid graphs,” in Proceedings of the 38th Annual Symposium on Foundations of Computer Science (FOCS ’97), pp. 496-505, 1997. |

[14] | A. N. M. Salman, Contributions to graph theory, Ph.D. thesis, University of Twente, 2005. |

[15] | K. Islam, H. Meijer, Y. Nunez, D. Rappaport, and H. Xiao, “Hamiltonian circuts in hexagonal grid graphs,” in Proceedings of the CCCG, pp. 20-22, 2007. |

[16] | V. S. Gordon, Y. L. Orlovich, and F. Werner, “Hamiltonian properties of triangular grid graphs,” Discrete Mathematics, vol. 308, no. 24, pp. 6166-6188, 2008. · Zbl 1158.05040 |

[17] | M. Nandi, S. Parui, and A. Adhikari, “The domination numbers of cylindrical grid graphs,” Applied Mathematics and Computation, vol. 217, no. 10, pp. 4879-4889, 2011. · Zbl 1223.05214 |

[18] | F. Keshavarz-Kohjerdi, A. Bagheri, and A. Asgharian-Sardroud, “A linear-time algorithm for the longest path problem in rectangular grid graphs,” Discrete Applied Mathematics, vol. 160, no. 3, pp. 210-217, 2012. · Zbl 1237.05115 |

[19] | F. Keshavarz-Kohjerdi and A. Bagheri, “An efficient parallel algorithm for the longest path problem in meshes,” http://arxiv.org/abs/1201.4459. · Zbl 1245.05081 |

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