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On Detours in Graphs1

Published online by Cambridge University Press:  20 November 2018

S. F. Kapoor ,
H.V. Kronk  and
D.R. Lick
S. F. Kapoor
Affiliation:
Western Michigan University, SUNY at Binghamton
H.V. Kronk
Affiliation:
Western Michigan University, SUNY at Binghamton
D.R. Lick
Affiliation:
Western Michigan University, SUNY at Binghamton
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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.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 2 , June 1968 , pp. 195 - 201
Copyright
Copyright © Canadian Mathematical Society 1968

Footnotes

1

The authors thank Professor Gary Chartrand for his helpful suggestions.

References

1. Chartrand, G., Geller, D. and Hedetniemi, S., Graphs with forbidden subgraphs. To appear.Google Scholar
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.Google Scholar
3. Ore, O., Theory of graphs (Chapters 2,3). Amer. Math. Soc. Colloq. Publ., 38 (Providence, 1962).Google Scholar
4. Ore, O., Hamiltonian connected graphs. J. Math. Pures Appl. 42 (1963) 21-27.Google Scholar