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Variations on the Hamiltonian Theme

Published online by Cambridge University Press:  20 November 2018

J. A. Bondy*
Affiliation:
University of Waterloo, Waterloo, Ontario
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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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1972

References

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.Google Scholar
2. Bondy, J. A., Large cycles in graphs, Discrete Mathematics 1 (1971), 121-132.Google Scholar
3. Chvátal, V., On Hamilton's ideals, Univ. of Waterloo preprint.Google Scholar
4. Gaudin, T., Herz, J.-C., and Rossi, P., Solution du Problème No. 29, Rev. Franc. Rech. Operationelle 8 (1964), 214-218.Google Scholar
5. Harary, F., Graph theory, Addison-Wesley, Reading, Mass., 1969.Google Scholar
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.Google Scholar
7. Lindgren, W. F., An infinite class of Hypo Hamiltonian graphs, Amer. Math. Monthly 74 (1967), 1087-1088.Google Scholar
8. Ore, O., Arc coverings of graphs, Ann. Mat. Pur. Appl. 55 (1961), 315-321.Google Scholar
9. Tutte, W. T., A non-Hamiltonian graph, Canad. Math. Bull. 3 (1960), 1-5.Google Scholar
10. Woodall, D. R., Sufficient conditions for circuits, J. London Math. Soc. (to appear).Google Scholar