The existence and upper bound for two types of restricted connectivity

Authors:
Qinghai Liu;Zhao Zhang
Affiliations:
College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang, 830046, People's Republic of China;College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang, 830046, People's Republic of China
Venue:
Discrete Applied Mathematics
Year:
2010

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Abstract

In this paper, we study two types of restricted connectivity: @k"k(G) is the cardinality of a minimum vertex cut S such that every component of G-S has at least k vertices; @k"k^'(G) is the cardinality of a minimum vertex cut S such that there are at least two components in G-S of order at least k. In this paper, we give some sufficient conditions for the existence and upper bound of @k"k(G) and/or @k"k^'(G), and study some properties of these two parameters.