Recent Advances on the Hamiltonian Problem: Survey III

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Abueida, A., Busch, A., Sritharan, R.: Hamiltonian spider intersection graphs are cycle extendable (preprint)

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Ainouche A.: Extensions of Bondy’s theorem on cycles in 2-connected graphs. Ars Combin. 85, 385–393 (2007)

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Bian Q., Horn P., Janiszewski S., La Fleur S., Gould R.J., Wrayno P.: 3-connected {K 1,3, P 9 }-free graphs are Hamiltonian connected. Graphs Combin. 313, 2772–2777 (2013)

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Bohman T., Frieze A.: Hamilton cycles in 3-out. Random Struct. Algorithms 35, 393–417 (2009)

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Broersma H., Ryjacek Z., Vrána P.: How many conjectures can you stand? A survey. Graphs Combin. 28, 57–75 (2012)

Broersma H., Xiong L., Yoshimoto K.: Toughness and Hamiltonicity in k-trees. Discrete Math. 307, 832–838 (2007)

Brousek J.: Forbidden triples for Hamiltonicity. Discrete Math. 251, 71–76 (2002)

Brunet, R., Nakamoto, A., Negami, S.: Every 5-connected triangulation of the Klein bottle is Hamiltonian. In: Proceedings of the 10th Workshop on Topological Graph Theory (Yokohama, 1998) Yokohama Mathematical Journal, vol. 47, pp. 239–244 (1999)

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Chen C.: Any maximal planar graph with only one separating triangle is Hamiltonian. J. Comb. Optim. 7, 79–86 (2003)

Chen B., Zhang S., Qiao Q.: Hamilton cycles in claw-heavy graphs. Discrete Math. 309, 2015–2019 (2009)

Chen G., Fan G., Yu X.: Cycles in 4-connected planar graphs. Eur. J. Combin. 25, 763–780 (2004)

Chen G., Faudree R.J., Gould R.J., Jacobson M.S.: Cycle extendability of Hamiltonian interval graphs. SIAM J. Discrete Math. 20, 682–689 (2006)

Chen G., Faudree R.J., Gould R.J., Jacobson M.S., Lesniak L., Pfender F.: Linear forests and ordered cycles. Discussiones Mathematicae Graph Theory 24, 359–372 (2004)

Chen G., Gould R.J.: Hamiltonian connected graphs involving forbidden subgraphs. Bull. Inst. Combin. Appl. 29, 25–32 (2000)

Chen G., Gould R.J., Pfender F.: New conditions for k-ordered Hamiltonian graphs. Ars Combin. 70, 245–255 (2004)

Christofides D., Kühn D., Osthus D.: Edge-disjoint Hamiltonian cycles in graphs. J. Combin. Theory Ser. B 102, 1035–1060 (2012)

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Cooper C., Frieze A., Krivelevich M.: Hamilton graphs in random graphs with a fixed degree sequence. SIAM J. Discrete Math. 24, 558–569 (2010)

Cuckler B., Kahn J.: Hamiltonian cycles in Dirac graphs. Combinatorica 29, 299–326 (2009)

Cui Q., Hu Y., Wang J.: Long cycles in 4-connected planar graphs. Discrete Math. 309, 1051–1059 (2009)

Diaz J., Mitsche D., Pérez X.: Sharp threshold for Hamiltonicity of random geometric graphs. SIAM J. Discrete Math. 21, 57–65 (2007)

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Dudek A., Frieze A.: Tight Hamilton cycles in random uniform hypergraphs. Random Struct. Algorithms 42, 374–385 (2012)

Dudek, A., Frieze, A., Loh, P.-S., Speiss, S.: Optimal divisibility conditions for loose Hamilton cycles in random hypergraphs. Electron. J. Combin. 19 (2012), Paper 44

Dudek, A., Frieze, A., Rucinski, A.: Rainbow Hamilton cycles in uniform hypergraphs. Electron. J. Combin. 19 (2012), Paper 46

Duffus, D., Gould, R.J., Jacobson, M.S.: Forbidden subgraphs and the Hamiltonian theme. In: Chartrand, Alavi, Goldsmith, Lesniak, Lick (eds.) The Theory and Applications of Graphs, (Kalmazoo, Mich., 1980), pp. 297–316. Wiley, New York (1981)

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Efthymiou, C., Spitakas, P.G.: On the existence of Hamiltonian cycles in random intersection graphs. Lecture Notes in Computer Science, pp. 690–701. Springer, Berlin (2005)

Efthymiou C., Spirakas P.G.: Sharp thresholds for hamiltonicity in random intersection graphs. Theor. Comput. Sci. 411, 3714–3730 (2010)

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Faudree J.R., Faudree R.J.: Hamiltonian cycles containing ordered linear forests. Bull. Inst. Combin. Appl. 5, 78–104 (2009)

Faudree J.R., Faudree R.J., Gould R.J., Jacobson M.S., Lesniak L.: On k-ordered graphs. J. Graph Theory 35, 69–82 (2000)

Faudree J.R., Faudree R.J., Ryjáčk Z., Vrána P.: On forbidden pairs implying Hamilton-connectedness. J. Graph Theory 72, 327–345 (2013)

Faudree R.J., Gould R.J.: Characterizing forbidden pairs for Hamiltonian properties. Discrete Math. 173, 45–60 (1997)

Faudree R.J., Gould R.J., Jacobson M.J., Lesniak L.: Characterizing forbidden clawless triples implying Hamiltonian graphs. Discrete Math. 249, 71–81 (2002)

Faudree R.J., Gould R.J., Jacobson M.S.: Forbidden triples implying hamiltonicity: for all graphs. Discuss. Math. Graph Theory 24, 47–54 (2004)

Faudree R.J., Gould R.J., Jacobson M.S.: Potential forbidden triples implying Hamiltonicity: for sufficiently large graphs. Discuss. Math. Graph Theory 25, 273–289 (2005)

Faudree R.J., Gould R.J., Jacobson M.S., Lesniak L.: Minimum degree and (k,m)-pancyclic ordered graphs. Graphs Combin. 21, 197–211 (2005)

Faudree R.J., Gould R.J., Kostochka A., Lesniak L., Schiermeyer I., Saito A.: Degree conditions for k-ordered Hamiltonian graphs. J. Graph Theory 42, 199–210 (2003)

Faudree, R.J., Gould, R.J., Jacobson, M.S.: Pancyclic graphs and linear forests. Discrete Math. (2013, to appear)

Faudree R.J., Gould R.J., Jacobson M.S., Magnant C.: Distributing vertices on Hamiltonian cycles. J. Graph Theory 69, 28–45 (2012)

Faudree, R.J., Gould, R.J.: Precise location of vertices on Hamiltonian cycles. Discrete Math. 313(23), 2772–2777 (2013)

Faudree R.J., Gould R.J., Jacobson M.S., Lesniak L.: Generalizing pancyclic and k-ordered graphs. Graphs Combin. 20, 291–309 (2004)

Faudree, R.J., Lehel, J., Yoshimoto, K.: A note on locating pairs of vertices on a Hamiltonian cycle (preprint)

Favaron O., Flandrin E., Li H., Tian F.: An Ore-type condition for pancyclability. Discrete Math. 206, 139–144 (1999)

Ferrara M., Gould R.J., Jacobson M.S., Pfender F., Powell J., Whalen T.: New Ore-type conditions for H-linked graphs. J. Graph Theory 71, 69–77 (2012)

Ferrara M., Gould R.J., Tansey G., Whalen T.: Disjoint Hamiltonian cycles in bipartite graphs. Discrete Math. 309, 3811–3820 (2009)

Ferrara M., Gould R.J., Tansey G., Whalen T.: On H-linked graphs. Graphs Combin. 22, 217–224 (2006)

Ferrara M., Jacobson M.S., Harlan A.: Hamiltonian cycles avoiding sets of edges in a graph. Australas. J. Combin. 48, 191–203 (2010)

Ferrara M., Magnant C., Powell J.: Pan-H-linked graphs. Graphs Combin. 26, 225–242 (2010)

Fiedler M., Nikiforov V.: Spectral radius and hamiltonicity of graphs. Linear Algebra Appl. 432, 2170–2173 (2010)

Flandrin E., Li H., Marczyk A., Wožniak M.: A note on pancyclism of highly connected graphs. Discrete Math. 286, 57–60 (2004)

Florek J.: On Barnette’s conjecture. Discrete Math. 310, 1531–1535 (2010)

Frankl P., Katona Gy.Y.: Extremal k-edge Hamiltonian hypergraphs. Discrete Math. 308, 1415–1424 (2008)

Frieze, A.: Loose Hamilton cycles in random 3-uniform hypergraphs. Electron. J. Combin. 17, #N283 (2010)

Frieze A., Krivelevich M.: On packing Hamilton cycles in ε-regular graphs. J. Combin. Theory B 94, 159–172 (2005)

Frieze A., Krivelevich M., Loh P.-S.: Packing tight Hamilton cycles in 3-uniform hypergraphs. Random Struct. Algorithms 40, 269–300 (2012)

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Fujisawa J., Nakamoto A., Ozeki K.: Hamiltonian cycles in bipartite toroidal graphs with a partite set of degree four vertices. J. Combin. Theory B 103, 46–60 (2013)

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Glebov R., Krivelevich M.: On the number of Hamilton cycles in sparse random graphs. SIAM J. Discrete Math. 27, 27–42 (2013)

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Gould R.J., Whalen T.: Subdivision extendibility. Graphs Combin. 23, 165–182 (2007)

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