Abstract
AbstractLet t be a positive real number. A graph is called t-tough if the removal of any vertex set S that disconnects the graph leaves at most |S|/t components. The toughness of a graph is the largest t for which the graph is t-tough. We prove that toughness is fixed-parameter tractable parameterized with the treewidth. More precisely, we give an algorithm to compute the toughness of a graph G with running time $${\mathcal {O}}(|V(G)|^3\cdot \textrm{tw}(G)^{2\textrm{tw}(G)})$$
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where $$\textrm{tw}(G)$$
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is the treewidth. If the treewidth is bounded by a constant, then this is a polynomial algorithm.
Funder
National Research, Development and Innovation Office
Publisher
Springer Science and Business Media LLC
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