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Cycles and Connectivity in Graphs

Published online by Cambridge University Press:  20 November 2018

M. E. Watkins  and
D. M. Mesner
M. E. Watkins
Affiliation:
University of North Carolina, Chapel Hill, North Carolina
D. M. Mesner
Affiliation:
University of North Carolina, Chapel Hill, North Carolina
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In this note, G will denote a finite undirected graph without multiple edges, and V = V(G) will denote its vertex set. The largest integer n for which G is n-vertex connected is the vertex-connectivity of G and will be denoted by λ = λ(G). One defines ζ to be the largest integer z not exceeding |V| such that for any set U ⊂ V with |U| = z, there is a cycle in G which contains U. The symbol i(U) will denote the component index of U. As a standard reference for this and other terminology, the authors recommend O. Ore (3).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 1319 - 1328
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Dirac, G. A., In abstrakten Graphen vorhandene vollständige 4-Graphen und ihre Unterteilungen, Math. Nachr., 22 (1960), 61–85.Google Scholar
2. Dirac, G. A., Généralisations du théorème de Menger, C. R. Acad. Sci. Paris, 250 No. 26, (1960), 4252–4253.Google Scholar
3. Ore, O., Theory of graphs (Providence, R.I., 1962).Google Scholar