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A sufficient condition for n-connectedness of graphs

Published online by Cambridge University Press:  26 February 2010

Gary Chartrand ,
S. F. Kapoor  and
Hudson V. Kronk
Gary Chartrand
Affiliation:
Western Michigan University, Kalamazoo. Michigan
S. F. Kapoor
Affiliation:
Western Michigan University, Kalamazoo. Michigan
Hudson V. Kronk
Affiliation:
Western Michigan University, Kalamazoo. Michigan
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Extract

A graph G (finite, undirected, and without loops or multiple lines) is n-connected if the removal of fewer than n points from G neither disconnects it nor reduces it to the trivial graph consisting of a single point. We present in this note a sufficient set of conditions on the degrees (valences) of the points of a graph G so that G is n-connected.

Type
Research Article
Information
Mathematika , Volume 15 , Issue 1 , June 1968 , pp. 51 - 52
Copyright
Copyright © University College London 1968

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References

1.Chartrand, G. and Harary, F., “Graphs with prescribed connectivities”, 1966 Symp. on Graph Theory, Tihany, Acad. Sci. Hung., 1967, 61–63.Google Scholar
2.Pósa, L., “A theorem concerning Hamiltonian lines”, Magyar Tud. Akad. Mat. Kutató Int. Közl., 7 (1962), 225–226.Google Scholar