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Maximum graphs non-Hamiltonian-connected from a vertex

Published online by Cambridge University Press:  18 May 2009

G. R. T. Hendry
G. R. T. Hendry
Affiliation:
University Of Aberdeen
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A path (cycle) in a graph G is called a hamiltonian path (cycle) of G if it contains every vertex of G. A graph is hamiltonian if it contains a hamiltonian cycle. A graph G is hamiltonian-connectedif it contains a u-vhamiltonian path for each pair u, v of distinct vertices of G. A graph G is hamiltonian-connected from a vertex v of G if G contains a v-whamiltonian path for each vertex w≠v. Considering only graphs of order at least 3, the class of graphs hamiltonian-connected from a vertex properly contains the class of hamiltonian-connected graphs and is properly contained in the class of hamiltonian graphs.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 25 , Issue 1 , January 1984 , pp. 97 - 98
Copyright
Copyright © Glasgow Mathematical Journal Trust 1984

References

REFERENCES

1.Bondy, J. A., Variations on the Hamiltonian theme, Canad. Math. Bull. 15 (1972), 57–62.CrossRefGoogle Scholar
2.Chartrand, G. and Nordhaus, E. A., Graphs Hamiltonian-connected from a vertex, The theory and applications of graphs, edited by Chartrand, G. et al. (John Wiley, 1981), 189–201.Google Scholar
3.Ore, O., Hamilton connected graphs, J. Math. Pures Appl. 42 (1963), 21–27.Google Scholar
4.Ore, O., Note on Hamilton circuits, Amer. Math. Monthly 67 (1960), 55.CrossRefGoogle Scholar