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Pré-Publication, Document De Travail Année : 2019

Parameterized Algorithms for Finding Square Roots

Résumé

We show that the following two problems are fixed-parameter tractable with parameter k: testing whether a connected n-vertex graph with m edges has a square root with at most n − 1 + k edges and testing whether such a graph has a square root with at least m − k edges. Our first result implies that squares of graphs obtained from trees by adding at most k edges can be recognized in polynomial time for every fixed k ≥ 0; previously this result was known only for k = 0. Our second result is equivalent to stating that deciding whether a graph can be modified into a square root of itself by at most k edge deletions is fixed-parameter tractable with parameter k.
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Dates et versions

hal-02332212 , version 1 (24-10-2019)

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  • HAL Id : hal-02332212 , version 1

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Manfred Cochefert, Jean-François Couturier, Petr A. Golovach, Dieter Kratsch, Daniël Paulusma. Parameterized Algorithms for Finding Square Roots. 2019. ⟨hal-02332212⟩
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