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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A note on $k$-critically $n$-connected graphs
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by R. C. Entringer and Peter J. Slater PDF
Proc. Amer. Math. Soc. 66 (1977), 372-375 Request permission

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
  • © Copyright 1977 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 66 (1977), 372-375
  • MSC: Primary 05C99
  • DOI: https://doi.org/10.1090/S0002-9939-1977-0476580-4
  • MathSciNet review: 0476580