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Variations on the Hamiltonian Theme

  • J. A. Bondy (a1)
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As its name implies, this paper consists of observations on various topics in graph theory that stem from the concept of Hamiltonian cycle. We shall mainly adopt the notation and terminology of Harary [5]. However, we use vertices and edges for what are called "points" and "lines" in [5]. V(G), E(G) respectively will denote the sets of vertices and edges of graph G, and |X| will denote the cardinal of the set X.|V(G)| is the order of G, and |E(G)| the size of G. Throughout n is reserved for the order of G.

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References
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1. Bondy, J. A., Large cycles in graphs, Proc. of the First Louisiana Conference on Combinatorics, Graph Theory, and Computing, Louisiana State Univ., 1970 (ed. Mullin, R. C., Reid, K. B., Roselle, D. P.), 47-60.
2. Bondy, J. A., Large cycles in graphs, Discrete Mathematics 1 (1971), 121-132.
3. Chvátal, V., On Hamilton's ideals, Univ. of Waterloo preprint.
4. Gaudin, T., Herz, J.-C., and Rossi, P., Solution du Problème No. 29, Rev. Franc. Rech. Operationelle 8 (1964), 214-218.
5. Harary, F., Graph theory, Addison-Wesley, Reading, Mass., 1969.
6. Herz, J.-C., Duby, J.-J., and Vigué, F., Recherche systématique des graphes hypoHamiltoniens, in Theory of Graphs, Internat. Symposium, Rome (1966), (ed. P. Rosenstiehl), 153-159.
7. Lindgren, W. F., An infinite class of Hypo Hamiltonian graphs, Amer. Math. Monthly 74 (1967), 1087-1088.
8. Ore, O., Arc coverings of graphs, Ann. Mat. Pur. Appl. 55 (1961), 315-321.
9. Tutte, W. T., A non-Hamiltonian graph, Canad. Math. Bull. 3 (1960), 1-5.
10. Woodall, D. R., Sufficient conditions for circuits, J. London Math. Soc. (to appear).
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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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