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On feedback vertex sets and nonseparating independent sets in cubic graps. (English) Zbl 0657.05042
A subset F, J of nodes of G (undirected, connected with n nodes) is a FVS (feedback vertex set) if G-F is a forest, a NSIS (nonseparating independent set) if no two nodes of J are adjacent and G-J is connected, respectively. The equation \(f(G)=n/2-z(G)+1,\) where f, z denotes the cardinality of min FVS, max NSIS, respectively, and two new upper bounds for f(G) are derived for cubic graphs G.
Reviewer: J.Štulc

MSC:
05C35 Extremal problems in graph theory
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[1] Garey, SIAM J. Appl. Math. 32 pp 826– (1977)
[2] On vertex-induced forests in cubic graphs. Proceedings of the 5th South East Conference on Combinatorics, Graph Theory, and Computing (1974) 501–512.
[3] and , Some further approximation algorithms for the vertex cover problem. Proceedings of the 8th Colloquium on Trees in Algebra and Programming (1983) 341–349.
[4] Simonovits, Acta Math. Acad. Sci. Hung. 18 pp 191– (1967)
[5] Bounds on feedback vertex sets of undirected cubic graphs. Coll. Math. Soc. Janos Bolyai 42. Algebra, Combinatorics and Logic in Computer Science (1983) 719–729.
[6] Untersuchungen zum Feedback Vertex Set Problem in ungerichteten Graphen. Ph.D. thesis, Paderborn (1983). · Zbl 0534.68046
[7] Staton, Discrete Math. 49 pp 175– (1984)
[8] and , Über Kreise in Graphen. VEB Deutscher Verlag der Wissenschaften, Berlin (1974). · Zbl 0288.05101
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