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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on $ k$-critically $ n$-connected graphs


Authors: R. C. Entringer and Peter J. Slater
Journal: Proc. Amer. Math. Soc. 66 (1977), 372-375
MSC: Primary 05C99
MathSciNet review: 0476580
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Abstract: A graph G is said to be $ ({n^\ast},k)$-connected if it has connectivity n and every set of k vertices is contained in an n-cutset. It is shown that an $ ({n^\ast},k)$-connected graph G contains an n-cutset C such that G -- C has a component with at most $ n/(k + 1)$ vertices, thereby generalizing a result of Chartrand, Kaugars and Lick. It is conjectured, however, that $ n/(k + 1)$ can be replaced with $ n/2k$ and this is shown to be best possible.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0476580-4
PII: S 0002-9939(1977)0476580-4
Keywords: n-connected, critical, graph, component
Article copyright: © Copyright 1977 American Mathematical Society