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On Detours in Graphs1

  • S. F. Kapoor (a1), H.V. Kronk (a1) and D.R. Lick (a1)
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A path of maximum length in a graph G is referred to as a detour path of G and the length of such a path is called the detour number of G. It is not surprising that the study of detour paths is closely associated with the problem of investigating hamiltonian paths in graphs. Evidently few results have been obtained in this area, although Ore [3] has shown that any two detour paths intersect. It is the purpose of this article to further investigate these concepts. In particular, we obtain bounds for several graph theoretic parameters in terms of the detour number and also present formulae for the detour numbers of several important classes of graphs.

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1

The authors thank Professor Gary Chartrand for his helpful suggestions.

Footnotes
References
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1. Chartrand, G., Geller, D. and Hedetniemi, S., Graphs with forbidden subgraphs. To appear.
2. Herz, J. C., Duby, J.J. and Vigué, F., Recherche systématique des graphes hypohamiltoniens. Théorie des graphes, journées internationales d'études. (Dunod, Paris, 1967) 153-159.
3. Ore, O., Theory of graphs (Chapters 2,3). Amer. Math. Soc. Colloq. Publ., 38 (Providence, 1962).
4. Ore, O., Hamiltonian connected graphs. J. Math. Pures Appl. 42 (1963) 21-27.
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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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