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Igor Fabrici, Erhard Hexel and Stanislav Jendrol’

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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Fan Wang and Weisheng Zhao

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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Ruijuan Li and Tingting Han

.2307/2315334 [8] J. Huang, On the structure of local tournaments , J. Combin. Theory Ser. B 63 (1995) 200–221. doi:10.1006/jctb.1995.1016 [9] S. Li, W. Meng, Y. Guo and G. Xu, A local tournament contains a vertex whose out-arc are pseudo-girth-pancyclic , J. Graph Theory 62 (2009) 346–361. doi:10.1002/jgt.20404 [10] D. Meierling, Local tournaments with the minimum number of Hamiltonian cycles or cycles of length three , Discrete Math. 310 (2010) 1940–1948. doi:10.1016/j.disc.2010.03.003 [11] C. Thomassen, Edge-disjoint Hamiltonian paths and cycles in

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Erhard Hexel

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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Ben Seamone

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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Juan José Montellano-Ballesteros and Anahy Santiago Arguello

, Berlin-New York, 1981) 23–34. [5] E. Durnberger, Connected Cayley graphs of semi-direct products of cyclic groups of prime order by abelian groups are hamiltonian , Discrete Math. 46 (1983) 55–68. doi:10.1016/0012-365X(83)90270-4 [6] E. Ghaderpour and D. Witte Morris, Cayley graphs on nilpotent groups with cyclic commutator subgroup are hamiltonian , Ars Math. Contemp. 7 (2014) 55–72. doi:10.26493/1855-3974.280.8d3 [7] H.H. Glover, K. Kutnar, A. Malnič and D. Marušič, Hamilton cycles in (2, odd, 3) - Cayley graphs , Proc. Lond. Math. Soc

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Olga Bodroža-Pantić, Harris Kwong, Rade Doroslovački and Milan Pantić

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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Thomas M. Lewis

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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Vojtech Rödl and Andrzej Ruciński

References [1] R. Aharoni, A. Georgakopoulos and P. Sprüssel, Perfect matchings in r-partite r- graphs, European J. Combin. 30 (2009) 39-42. doi:10.1016/j.ejc.2008.02.011 [2] E. Buss, H. H`an and M. Schacht, Minimum vertex degree conditions for loose Hamil- ton cycles in 3-uniform hypergraphs, J. Combin. Theory (B), to appear. [3] R. Glebov, Y. Person andW.Weps, On extremal hypergraphs for hamiltonian cycles, European J. Combin. 33 (2012) 544-555 (An extended abstract has appeared in the Proceedings of EuroComb

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Charles Brian Crane

P. Zhang, Graphs and Digraphs, 5 th Edition (Chapman and Hall/CRC, Boca Raton, FL, 2011). [5] C.B. Crane, Generalized pancyclic properties in claw-free graphs , Graphs Combin. 31 (2015) 2149–2158. doi:10.1007/s00373-014-1510-5 [6] Y. Egawa, J. Fujisawa, S. Fujita and K. Ota, On 2 -factors in r-connected { K 1, k , P 4 } -free graphs , Tokyo J. Math. 31 (2008) 415–420. doi:10.3836/tjm/1233844061 [7] R.J. Faudree and R.J. Gould, Characterizing forbidden pairs for Hamiltonian properties , Discrete Math. 173 (1997) 45–60. doi:10.1016/S