參考文獻 |
[1] D. Amar, I. Fournier, and A. Germa, ``Pancyclism in Chv¶atal-Erd}os graphs," Graphs Combinat., Vol. 7, pp. 101-112, 1991.
[2] B. Alspach, ``Hamiltonian cycles in vertex-transitive graphs of order 2p," Second International Conference on Combinat. Math., pp. 131-139, 1978.
[3] B. Alspach, and D. Hare, ``Edge-pancyclic block-intersection graphs," Discrete Math., Vol. 97, pp. 17-24, 1979.
[4] L. Babai, Problem 17, unsolved problems, Summer Research Workshop in Algebraic Combinatorics, Simon Fraser University, July 1979.
[5] K. S. Bagga and B. Varma, Bipartite graphs and degree conditions," in: Graph Theory, Combinatorics, Algorithms and Applications, Proc. 2nd Int. Conf. san Francisco,CA, 1989, 1991, pp. 564-573.
[6] J. S. Bagga, and B. N. Varma, ``Hamiltonian properties in bipartite graphs," Syst. Sci. and Math. Sci. , Vol. 26, pp. 71-85, 1999.
[7] D. Bauer, H. J. Broersma, H. J. Veldman, and L. Rao, ``A generalization of a result of HÄaggkvist and Nicoghossian," J. Combinat. Theory B, Vol. 47, pp. 237-243, 1989.
[8] D. Bauer, A. Morgana, E. Schmeichel, and H. J. Veldman, ``Long cycles in graphs with large degree sums," Discrete Math., Vol. 79, pp. 59-70, 1990.
[9] D. Bauer, H. J. Broersma, and H. J. Veldman, ``Not every 2-tough graph is Hamiltonian," Discrete Appl. Math., Vol. 99, pp. 317-321, 2000.
[10] J. A. Bondy, ``Longest paths and cycles in graphs of high degree," Research Report CORR 80{16, Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, Canada, 1980.
[11] J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, North Holland, New York, 1980.
[12] J. A. Bondy, ``Pancyclic graphs I," J. Combinat. Theory, Vol. 11, pp. 80-84, 1971.
[13] H. J. Broersma, J. van den Heuvel, B. Jackson, and H. J. Veldman, ``Hamiltonian of regular 2-connected graphs," J. Graph Theory, Vol. 22, pp. 105-124, 1996.
[14] M. Y. Chan and S. J. Lee, ``On The Existence of Hamiltonian Circuits in Faulty Hypercubes," SIAM J. Discrete Math., Vol. 4, pp. 511-527, 1991.
[15] C. H. Chang, C. K. Lin, H. M. Huang, and L. H. Hsu, ``The super laceability of hypercubes," Information Processing Letters, Vol. 92, pp. 15-21, 2004.
[16] Y. H. Chang, C. N. Hung, and C. M. Sun, ``Adjacent vertices fault tolerant hamiltonian laceability of hypercube graphs," Proceedings of the 22nd Workshop on Combinatorial Mathematics and Computation Theory, pp. 301-309, 2005.
[17] C. Cooper, A. Frieze, and B. Reed, ``Random regular graphs of non-constant degree: connectivity and hamiltonicity," Combinat. Probability and Computing , Vol. 11, pp. 249-261, 2002.
[18] V. Chv¶atal and P. ErdÄos, ``A note on hamiltonian circuits," Discrete math., Vol. 5, pp. 111-113, 1972.
[19] V. Chv¶atal, ``Tough graphs and hamiltonian circuits," Discrete math., Vol. 5, pp. 215-228, 1973.
[20] G. A. Dirac, ``Some theorems on abstract graphs," Proc. London Math. Soc., Vol. 2, pp. 69-81, 1952.
[21] D. A. Du®us, R. J. Gould, and M. S. Jacobson, ``Forbidden subgraphs and the Hamiltonian theme," Theory and Applications of Graphs, Wiley, New York, pp. 297-316, 1981.
[22] Y. Egawa and T. Miyamoto, ``The longest cycles in a graph G with minimum degree at least |G|/k," J. Combinat. Theory B, Vol. 46, pp. 356-362, 1989.
[23] B. Enomoto, B. Jackson, P. Katerinis, and A. Saito, ``Toughness and the existence of k-factors," J. Graph Theory, Vol. 9, pp. 87-95, 1985.
[24] H. Enomoto , A. Kaneko, A. Saito, and B. Wei, ``Long cycles in triangle-free graphs with prescribed independence number and connectivity," J. Combinat. Theory B, Vol. 91, pp. 43-55, 2004.
[25] G. Fan, ``Longest cycles in regular graphs," J. Combinat. Theory B, Vol. 39, pp. 325-345, 1985.
[26] R. J. Faudree, R. J. Gould, M. S. Gould, M. S. Jacobson , and R. H. Schelp, ``Neighborhood unions and hamiltonian properties in graphs," J. Combinat. Theory B, Vol. 47, pp. 1-9, 1989.
[27] T. I. Fenner and A. M. Frieze, ``Halmiltonian cycle in random graphs," J. Combinat. Theory B, Vol. 37, pp. 103-112, 1984.
[28] E. Flandrin, I. Fournier, and A. Germa, ``Pancyclism in K_{1,3}-free graphs," Ph.D. Thesis, 1990.
[29] E. Flandrin, J. L. Fouquet, and H. Li, ``Halmiltonian of bipartite biclaw-free graphs," Discrete Appl. Math., Vol. 51, pp. 95-102, 1994.
[30] H. Fleischner, ``The square of every two-connected graph is hamiltonian," J. Combinat. Theory B, Vol. 16, pp. 29-34, 1974.
[31] H. Fleischner, ``In the square of graphs, hamiltonianicity and pancyclicity, hamiltonian connectedness and panconnectedness are equivalent concepts ," Monatsh. Math., Vol. 82, pp. 125-149, 1976.
[32] J. S. Fu, ``Fault-tolerant cycle embedding in the hypercube," Parallel Computing, Vol. 29, pp. 821-832, 2003.
[33] J. S. Fu, ``Longest fault-free paths in hypercubes with vertex faults," Information Sciences, Vol. 176, pp. 756-771, 2006.
[34] S. Goodman, and S. Hedetniemi, ``Sufficient conditions for a graph to be hamiltonian," J. combinat. Theory B, Vol. 16, pp. 175-180, 1974.
[35] R. J. Gould, ``Updating the hamiltonian problem-a survey," J. Graph Theory, Vol. 15, no. 2, pp. 121-157, 1991.
[36] R. HÄaggkvist, ``Unsolved problem," Proceedings of Fifth Hungarian Colloquim on Combinat., 1976.
[37] R. HÄaggkvist and G. G. Nicoghossian, ``A remark on hamiltonian cycles," J. Combinat. Theory B, Vol. 30, pp. 118-120, 1981.
[38] J. P. Hayes, ``A graph model for fault-tolerant computing systems," IEEE Transactions on computers, Vol. c25, pp. 875-884, 1976.
[39] A. Hobbs, ``The square of a block is vertex pancyclic," J. combinat. Theory B, Vol. 20, pp. 1-4, 1976.
[40] D. A. Holton, B. Manvel, and B. D. Mckay, ``Hamiltonian cycles in cubic 3-connected bipartite planar graphs," J. Combinat. Theory B, Vol. 38, pp. 279-295, 1985.
[41] S. Y. Hsieh, G. H. Chen, and C. W. Ho, ``Hamiltonian-laceability of star graphs," Networks, Vol. 36, pp. 225-232, 2000.
[42] S. Y. Hsieh, ``Fault-tolerant cycle embedding in the hypercubes with more both faulty vertices and faulty edges," Parallel Computing, Vol. 32, pp. 84-91, 2006.
[43] B. Jackson and H. Li, ``Hamiltonian cycles in 2-connected regular bipartite graphs," J. Combinat. Theory B, Vol. 62, pp. 236-258, 1994.
[44] H. A. Jung, ``On maximal circuits in ¯nite graphs," Ann. Discrete Math., Vol. 3, pp. 129-144, 1978.
[45] J. K¶omlos and E. Szemer¶edi, ``Limit distribution for the existence of hamiltonian cycles in random graphs," Discrete Math., Vol. 43, pp. 55-63, 1983.
[46] M. Lewinter and W. Widulski, ``Hyper-hamilton laceable and caterpillar-spannable product graphs," Comput. Math. Appl., Vol. 34, pp. 99-104, 1997.
[47] M. Li, ``Longest cycles in regular 2-connected claw-free graphs," Discrete Math., Vol. 137, pp. 277-295, 1995.
[48] F. Thomson Leighton, Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes, Morgan Kaufmann, Los Altos, CA, 1992.
[49] T. K. Li, C. H. Tsai, Jimmy J. M. Tan, and L. H. Hsu, ``Bipanconnected and edge-fault-tolerant bipancyclic of hypercubes," Information Processing Letters, Vol. 87, pp. 107-110, 2003.
[50] C. K. Lin, H. M. Huang, L. H. Hsu and S. Bau, ``Mutually Hamiltonian paths in Star Networks," Networks., Vol. 46, pp. 110-117, 2005.
[51] C. K. Lin, H. M. Huang, J. J. M. Tan and L. H. Hsu, ``The Mutually Hamiltonian Cycles of the Pancake Networks and the Star Networks," submitted.
[52] X. Liu, ``lower bounds of length of longest cycles in graphs involving neighborhood unions ," Discrete Math., Vol. 169, pp. 133-144, 1997.
[53] M. Lipman, ``Hamiltonian cycles and paths in vertex-transitive graphs with abelian and nilpotent groups," Discrete math., Vol. 54, pp. 15-21, 1985.
[54] L. Lov¶asz, Combinatorial Structutres and Their Applications. Gordon and Breach, London ``Problem 11," 1970.
[55] D. Marusic, ``Hamiltonian paths in vertex-symmetric graphs of order 5p," Discrete math., Vol. 42, pp. 227-242, 1982.
[56] J. Mitchem and E. Schmeichel, ``Pancyclic and bipancyclic graphs-a survey," Graphs and Applications, pp. 271-278, 1982.
[57] M. M. Matthews, and D. P. Sumner, ``Longest paths and cycles in K1;3-free graphs," J. Graph Theory, Vol. 9, pp. 269-277, 1985.
[58] J. Moon and M. Moser, ``On hamiltonian bipartite graphs," Israel J. Math., Vol. 1, pp. 357-369, 1963.
[59] O. Ore, ``A note on hamiltonian circuits," Am. Math. Month., Vol. 67, pp. 55, 1960.
[60] O. Ore, ``Hamiltonian connected graphs," J. Math. Pures Appl., Vol. 42, pp. 21-27, 1963.
[61] O. Ordaz, D. Amar, and A. Raspaud, ``Hamiltonian properties and bipartite independence number," Discrete Math., Vol. 161, pp. 207-215, 1996.
[62] L. P¶osa, ``Hamiltonian circuits in random graphs," Discrete Math., Vol. 14, pp. 359-364, 1976.
[63] L. B. Richmond, R. W. Robinson, and N. C. Wormald, ``On hamiltonian cycles in 3-connected cubic maps," Ann. Discrete Math., Vol. 27, pp. 141-150, 1985.
[64] Y. Saad and M. H. Schultz, ``Topological properties of hypercubes," IEEE Transactions on Computers, Vol. 37, no. 7, pp. 867-872, 1988.
101
[65] A. Sengupta, ``On ring embedding in hypercubes with faulty nodes and links," Information Processing Letters, Vol. 68, pp. 207-214, 1998.
[66] G. Simmons, ``Almost all n-dimensional rectangular lattices are hamilton laceable," Congr. Numer., Vol. 21, pp. 649-661, 1978.
[67] J. E. Simpson, Hamiltonian bipartite graphs," Congr. Numer., Vol. 85, pp. 97-110, 1991.
[68] Z. M. Song, Y. S. Qin, ``A new su±cient condition for panconnected graphs," Ars Combin., Vol. 34, pp. 161-166, 1992.
[69] H. Trommel, H. J. Veldman, and A. Verschut, ``Pancyclicity of claw-free hamiltonian graphs ," Discrete Math., Vol. 197/198, pp. 781-789, 1999.
[70] Y. C. Tseng, ``Embedding a ring in a hypercube with both faulty links and faulty nodes," Information Processing Letter, Vol. 59, pp. 217-222, 1996.
[71] C. H. Tsai, J. M. Tan, T. Liang and L. H. Hsu, ``Fault-tolerant hamiltonian laceability of hypercubes," Information Processing Letters, Vol. 83, pp. 301-306, 2002.
[72] Chang-Hsiung Tsai, ``Linear array and ring embeddings in conditional faulty hypercubes," Theoretical Computer Science 314, pp. 431-443, 2004.
[73] A. S. Vaidya, P. S. N. Rao, and S. R. Shankar ``A class of hypercube-like networks," in: Pro. of the 5th Symp. On Parallel and Distributed Processing,IEEE Comput. Soc., Los alamitos, CA, December, pp. 800-803, 1993.
[74] B.Wei, ``Hamiltonian paths and hamiltonian connectivity in graphs," Discrete Math., Vol. 121, pp. 223-228, 1993.
[75] J. M. Xu, ``Edge-fault-tolerant edge-bipancyclicity of hypercubes," Information Processing Letter, Vol. 96, pp. 146-150, 2005.
[76] C. Q. Zhan, ``Hamiltonian cycles in claw-free graphs," J. Graph Theory, Vol. 12, pp. 209-216, 1988.
[77] C. Q. Zhang and Y. J. Zhu, ``Long path connectivity of regular graphs," Discrete Math., Vol. 96, pp. 151-160, 1991.
[78] Y. J. Zhu, Z. H. Liu, and Z. G. Yu, ``An improvement of Jackson's result on hamiltonian cycles in 2-connected regular graphs," Cycles in Graphs (Burnaby, B.C., 1982), North Holland Mathematics Studies, Vol. 115, North Holland, Amsterdam, pp. 237-247, 1985. |