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Improved Sufficient Conditions for Hamiltonian Properties

References [1] J.-P. Bode, A. Kemnitz, I. Schiermeyer and A. Schwarz, Generalizing Bondy’s theorems on sufficient conditions for Hamiltonian properties, Congr. Numer. 203 (2010) 5-13. [2] J.A. Bondy, Longest paths and cycles in graphs of high degree, Research Report CORR 80-16 (Department of Combinatorics and Optimization, Faculty of Mathe- matics, University of Waterloo, Waterloo, Ontario, Canada, 1980). [3] J.A. Bondy and V. Chvátal, A method in graph theory, Discrete Math. 15 (1976) 111-135. doi:10

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On Vertices Enforcing a Hamiltonian Cycle

References [1] C.A. Barefoot, Hamiltonian connectivity of the Halin graphs, Congr. Numer. 58 (1987) 93-102. [2] J.A. Bondy, Pancyclic graphs: recent results, in: Infinite and finite sets, Vol. 1, Colloq. Math. Soc. J´anos Bolyai 10, A. Hajnal, R. Rado and V.T. S´os (Ed(s)), (North Holland, 1975) 181-187. [3] J.A. Bondy and L. Lovász, Cycles through specified vertices of a graph, Combinatorica 1 (1981) 117-140. doi:10.1007/BF02579268 [4] H.J. Broersma and H.J. Veldman, 3-connected line

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On the Hamiltonian Number of a Plane Graph

References [1] M. Araya and G. Wiener, On cubic planar hypohamiltonian and hypotraceable graphs, Electron. J. Combin. 18 (2011) #P85. [2] T. Asano, T. Nishizeki and T. Watanabe, An upper bound on the length of a Hamil- tonian walk of a maximal planar graph, J. Graph Theory 4 (1980) 315-336. doi: 10.1002/jgt.3190040310 [3] J.-C. Bermond, On Hamiltonian walks, in: Proceedings of the Fifth British Combinatorial Conference, Util. Math., Winnipeg, Man. (1975) 41-51. [4] J.A. Bondy and U.S.R. Murty

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Hamiltonian Normal Cayley Graphs

R eferences [1] N. Alon and Y. Roichman, Random Cayley graphs and expanders , Random Structures Algorithms 5 (1994) 271–284. doi:10.1002/rsa.3240050203 [2] J.A. Bondy and U.S.R. Murty, Graph Theory (Springer, New York, 2008). [3] J. Bourgain and A. Gamburd, Uniform expansion bounds for Cayley graphs of SL 2 (ℱ p ), Ann. of Math. 167 (2008) 625–642. doi:10.4007/annals.2008.167.625 [4] C.C. Chen and N. Quimpo, On strongly hamiltonian abelian group graphs , Combin. Math. VIII (Geelong, 1980) Lecture Notes in Math. 884 (Springer

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On Uniquely Hamiltonian Claw-Free and Triangle-Free Graphs

References [1] S. Abbasi and A. Jamshed, A degree constraint for uniquely Hamiltonian graphs, Graphs Combin. 22 (2006) 433-442. doi:10.1007/s00373-006-0666-z [2] H. Bielak, Chromatic properties of Hamiltonian graphs, Discrete Math. 307 (2007) 1245-1254. doi:10.1016/j.disc.2005.11.061 [3] J.A. Bondy and B. Jackson, Vertices of small degree in uniquely Hamiltonian graphs, J. Combin. Theory (B) 74 (1998) 265-275. doi:10.1006/jctb.1998.1845 [4] R.C. Entringer and H. Swart, Spanning cycles of nearly

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On the Edge-Hyper-Hamiltonian Laceability of Balanced Hypercubes

References [1] J.A. Bondy and and U.S.R. Murty, Graph Theory with Applications (Macmillan Press, London, 1976). doi: 10.1007/978-1-349-03521-2 [2] R.X. Hao, R. Zhang, Y.Q. Feng and J.X. Zhou, Hamiltonian cycle embedding for fault tolerance in balanced hypercubes, Appl. Math. Comput. 244 (2014) 447-456. doi: 10.1016/j.amc.2014.07.015 [3] S.Y. Hsieh, G.H. Chen and C.W. Ho, Hamiltonian-laceability of star graphs, Net- works 36 (2000) 225-232. doi: 10.1002/1097-0037(200012)36:4h225::AID-NET3i3.0.CO;2-G

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Matchings Extend to Hamiltonian Cycles in 5-Cube

R eferences [1] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (North-Holland, New York-Amsterdam-Oxford, 1982). [2] R. Caha and V. Koubek, Spanning multi-paths in hypercubes , Discrete Math. 307 (2007) 2053–2066. doi:10.1016/j.disc.2005.12.050 [3] D. Dimitrov, T. Dvořák, P. Gregor and R. Škrekovski, Gray codes avoiding matchings , Discrete Math. Theoret. Comput. Sci. 11 (2009) 123–148. [4] T. Dvořák, Hamiltonian cycles with prescribed edges in hypercubes , SIAM J. Discrete Math. 19 (2005) 135–144. doi:10.1137/S

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Arc-Disjoint Hamiltonian Cycles in Round Decomposable Locally Semicomplete Digraphs

. Huang, Decomposing locally semicomplete digraphs into strong spanning subdigraphs , J. Combin. Theory Ser. B 102 (2012) 701–714. doi:10.1016/j.jctb.2011.09.001 [5] Y. Guo, Locally Semicomplete Digraphs (Ph.D. Thesis, RWTH Aachen University, 1995). [6] Y. Guo, Strongly Hamiltonian-connected locally semicomplet digraphs , J. Graph Theory 21 (1996) 65–73. doi:10.1002/(SICI)1097-0118(199605)22:1h65::AID-JGT9i3.0.CO;2-J [7] F. Harary and L. Moser, The theory of round robin tournaments , Amer. Math. Monthly 73 (1966) 231–246. doi:10

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On the H-Force Number of Hamiltonian Graphs and Cycle Extendability

R eferences [1] A. Abueida and R. Sritharan, Cycle extendability and Hamiltonian cycles in chordal graph classes , SIAM J. Discrete Math. 20 (2006) 669–681. doi:10.1137/S0895480104441267 [2] G. Chen, R.J. Faudree, R.J. Gould and M.S. Jacobson, Cycle extendability of Hamiltonian interval graphs , SIAM J. Discrete Math. 20 (2006) 682–689. doi:10.1137/S0895480104441450 [3] R. Diestel, Graph Theory (Springer, Graduate Texts in Mathematics 173 , 2005). [4] I. Fabrici, E. Hexel and S. Jendrol’, On vertices enforcing a Hamiltonian cycle

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A Limit Conjecture on the Number of Hamiltonian Cycles on Thin Triangular Grid Cylinder Graphs

R eferences [1] O. Bodroža-Pantić, B. Pantić, I. Pantić and M. Bodroža-Solarov, Enumeration of Hamiltonian cycles in some grid graphs , MATCH Commun. Math. Comput. Chem. 70 (2013) 181–204. [2] O. Bodroža-Pantić, H. Kwong and M. Pantić, Some new characterizations of Hamiltonian cycles in triangular grid graphs , Discrete Appl. Math. 201 (2016) 1–13. doi:10.1016/j.dam.2015.07.028 [3] O. Bodroža-Pantić, H. Kwong and M. Pantić, A conjecture on the number of Hamiltonian cycles on thin grid cylinder graphs , Discrete Math. Theoret. Comput. Sci

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