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arXiv · 1403.2796

The Algorithmic Complexity of Bondage and Reinforcement Problems in bipartite graphs

Fu-Tao Hu·Moo Young Sohn
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Abstract

Let $G=(V,E)$ be a graph. A subset $D\subseteq V$ is a dominating set if every vertex not in $D$ is adjacent to a vertex in $D$. The domination number of $G$, denoted by $\gamma(G)$, is the smallest cardinality of a dominating set of $G$. The bondage number of a nonempty graph $G$ is the smallest number of edges whose removal from $G$ results in a graph with domination number larger than $\gamma(G)$. The reinforcement number of $G$ is the smallest number of edges whose addition to $G$ results in a graph with smaller domination number than $\gamma(G)$. In 2012, Hu and Xu proved that the decision problems for the bondage, the total bondage, the reinforcement and the total reinforcement numbers are all NP-hard in general graphs. In this paper, we improve these results to bipartite graphs.

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Fu-Tao Hu, Moo Young Sohn. 2014-03-12. The Algorithmic Complexity of Bondage and Reinforcement Problems in bipartite graphs. https://arxiv.org/abs/1403.2796

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