Geodesic
On Detours in Graphs1
Canadian mathematical bulletin, Tome 11 (1968) no. 2, pp. 195-201

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Kapoor, S. F.; Kronk, H.V.; Lick, D.R. On Detours in Graphs1. Canadian mathematical bulletin, Tome 11 (1968) no. 2, pp. 195-201. doi: 10.4153/CMB-1968-022-8
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[1] 1. Chartrand, G., Geller, D. and Hedetniemi, S., Graphs with forbidden subgraphs. To appear. Google Scholar

[2] 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] 3. Ore, O., Theory of graphs (Chapters 2,3). Amer. Math. Soc. Colloq. Publ., 38 (Providence, 1962). Google Scholar

[4] 4. Ore, O., Hamiltonian connected graphs. J. Math. Pures Appl. 42 (1963) 21-27. Google Scholar

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