Tenacious Graph is NP-hard

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Moazzami Dara

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Journal Paper

Paper Information

Journal: JOURNAL OF ALGORITHMS AND COMPUTATION Year:2019 | Volume:51 | Issue:2 Page(s): 127-134

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Information Journal Paper

Title

Tenacious Graph is NP-hard

Author(s)

Moazzami Dara | Issue Writer Certificate

Keywords

minimum degree

complexity

tenacity

NP-hard

T-tenacious

Abstract

The tenacity of a graph G, T(G), is de ned by T(G) = minfjSj+ (G􀀀 S)! (G􀀀 S) g, where the minimum is taken over all vertex cutsets S of G. We de ne (G 􀀀 S) to be the number of the vertices in the largest component of the graph G 􀀀 S, and! (G 􀀀 S) be the number of components of G 􀀀 S. In this paper we consider the relationship between the minimum degree (G) of a graph and the complexity of recognizing if a graph is T-tenacious. Let T 1 be a rational number. We rst show that if (G) Tn T+1, then G is T-tenacious. On the other hand, for any xed > 0, we show that it is NP-hard to determine if G is T-tenacious, even for the class of graphs with (G) ( T T+1 􀀀 )n.

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APA: Copy

Moazzami, Dara. (2019). Tenacious Graph is NP-hard. JOURNAL OF ALGORITHMS AND COMPUTATION, 51(2), 127-134. SID. https://sid.ir/paper/354579/en

Vancouver: Copy

Moazzami Dara. Tenacious Graph is NP-hard. JOURNAL OF ALGORITHMS AND COMPUTATION[Internet]. 2019;51(2):127-134. Available from: https://sid.ir/paper/354579/en

IEEE: Copy

Dara Moazzami, “Tenacious Graph is NP-hard,” JOURNAL OF ALGORITHMS AND COMPUTATION, vol. 51, no. 2, pp. 127–134, 2019, [Online]. Available: https://sid.ir/paper/354579/en

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