Abstract
For a connected graph G, a set S of vertices is a cyclic vertex cutset if \(G - S\) is not connected and at least two components of \(G-S\) contain a cycle respectively. The cyclic vertex connectivity \(c \kappa (G)\) is the cardinality of a minimum cyclic vertex cutset. In this paper, for a 4-regular graph G with v vertices, we give a polynomial time algorithm to determine \(c \kappa (G)\) of complexity \(O(v^{15/2})\).
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Notes
In Dinitz (2006), Yefim Dinitz tells the differences between his version and Even’s Version.
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Acknowledgements
This work was supported by The Ph.D .Start-up Fund of Natural Science Foundation of Guangdong Province (Grant No. 2018A030310516), The Creative Talents Project Fund of Guangdong Province Department of Education (Natural Science) (Grant No. 2017KQNCX053), the Discovery Grant from the Natural Sciences and Engineering Research Council of Canada (Grant No. RGPIN-05317).
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Liang, J., Lou, D., Qin, Z. et al. A polynomial algorithm determining cyclic vertex connectivity of 4-regular graphs. J Comb Optim 38, 589–607 (2019). https://doi.org/10.1007/s10878-019-00400-6
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DOI: https://doi.org/10.1007/s10878-019-00400-6