Lattice graphs with non-concurrent longest cycles
Rendiconti del Seminario Matematico della Università di Padova, Tome 132 (2014), pp. 75-82. 
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     author = {Jumani, Ali Dino and Zamfirescu, Carol T. and Zamfirescu, Tudor I.},
     title = {Lattice graphs with non-concurrent longest cycles},
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     pages = {75--82},
     publisher = {Seminario Matematico of the University of Padua},
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     language = {en},
     url = {http://archive.numdam.org/item/RSMUP_2014__132__75_0/}
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Jumani, Ali Dino; Zamfirescu, Carol T.; Zamfirescu, Tudor I. Lattice graphs with non-concurrent longest cycles. Rendiconti del Seminario Matematico della Università di Padova, Tome 132 (2014), pp. 75-82. http://archive.numdam.org/item/RSMUP_2014__132__75_0/

[1] Y. Bashir - T. Zamfirescu, Lattice graphs with Gallai's property, Bull. Math. Soc. Sci. Math. Roumanie, 56 (2013), pp. 65–71. | MR | Zbl

[2] Y.-C. Chen - C.-H. Tsai - L.-H. Hsu - J. J. M. Tan, On some super fault-tolerant Hamiltonian graphs, Appl. Math. Comput., 148 (2004), pp. 729–741. | MR | Zbl

[3] T. Gallai, Problem 4, in: Theory of Graphs Proc. Tihany 1966 (eds.: P. Erdös & G. Katona), Academic Press, New York, 1968, p. 362. | MR

[4] J. P. Hayes, A Graph Model for Fault-Tolerant Computing Systems, IEEE Trans. Comput., 25 (1976), pp. 875–884. | MR | Zbl

[5] C.-N. Hung - L.-H. Hsu - T.-Y. Sung, On the Construction of Combined k -Fault-Tolerant Hamiltonian Graphs, Networks, 37 (2001), pp. 165–170. | MR | Zbl

[6] A. B. Kempe, A Memoir on the Theory of Mathematical Form, Phil. Trans. Roy. Soc. Lond., 177 (1886), pp. 170.

[7] B. Menke, Longest cycles in grid graphs, Studia Sci. Math. Hung., 36 (2000), pp. 201–230. | MR | Zbl

[8] B. Menke - Ch. Zamfirescu - T. Zamfirescu, Intersections of longest cycles in grid graphs, J. Graph Theory, 25 (1997), pp. 37–52. | MR | Zbl

[9] F. Nadeem - A. Shabbir - T. Zamfirescu, Planar lattice graphs with Gallai's property, Graphs Combin., 29 (2013), pp. 1523–1529. | MR | Zbl

[10] J.-H. Park - H.-C. Kim - H.-S. Lim, Fault-hamiltonicity of hypercube-like interconnection networks, Proc. of IEEE International Parallel and Distributed Processing Symposium IPDPS 2005, Denver, Apr. 2005.

[11] J.-H. Park - H.-S. Lim - H.-C. Kim, Panconnectivity and pancyclicity of hypercube-like interconnection networks with faulty elements, Theoret. Comput. Sci., 377 (2007), pp. 170–180. | MR | Zbl

[12] J. Petersen, Sur le théorème de Tait, L'Intermdiaire des Mathématiciens, 5 (1898), pp. 225–227.

[13] A. Shabbir - C. T. Zamfirescu - T. I. Zamfirescu, Intersecting longest paths and longest cycles: A survey, Electron. J. Graph Theory Appl., 1 (2013), pp. 56–76. | MR | Zbl

[14] A. Shabbir - T. Zamfirescu, Fault-tolerant designs in triangular lattice networks, submitted.

[15] H. Walther, Über die Nichtexistenz eines Knotenpunktes, durch den alle längsten Wege eines Graphen gehen, J. Combin. Theory, 6 (1969), pp. 16. | MR | Zbl

[16] T. Yamada - S. Ueno, Fault-tolerant graphs for tori, Networks, 32 (1998), pp. 181–188. | MR | Zbl

[17] T. Zamfirescu, A two-connected planar graph without concurrent longest paths, J. Combin. Theory, Ser. B, 13 (1972), pp. 116–121. | MR | Zbl

[18] T. Zamfirescu, On longest paths and circuits in graphs, Math. Scand., 38 (1976), pp. 211–239. | MR | Zbl

[19] T. Zamfirescu, Intersecting longest paths or cycles: a short survey, Analele Univ. Craiova, Ser. Mat.-Inf., 28 (2001), pp. 19. | MR | Zbl