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A polynomial time algorithm for cyclic vertex connectivity of cubic graphs

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Pages 1501-1514 | Received 12 May 2015, Accepted 25 Apr 2016, Published online: 26 Jul 2016
 

ABSTRACT

For a connected graph G, a set S of vertices is a cyclic vertex cutset if GS is not connected and at least two components contain a cycle respectively. The cyclic vertex connectivity cκ(G) is the cardinality of a minimum cyclic vertex cutset. In this paper, for any k-regular graph G with girth g and the number v of vertices, we give a sufficient condition v2g(k1) for the cyclic vertex connectivity cκ(G). Then we give a polynomial time algorithm to determine cκ(G) for a cubic graph G. The time complexity of the algorithm is bounded by O(v15/2).

2010 AMS SUBJECT CLASSIFICATIONS:

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1. In [Citation3], Yefim Dinitz tells the differences between his version and Even's Version.

Additional information

Funding

This research is partially supported by the China Scholarship Council [grant number 201508440189], and NSFC [grant number 11471003].

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