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arXiv · 1310.5469

Parameterized Algorithms for Finding Square Roots

Manfred Cochefert·Jean-François Couturier·Petr A. Golovach·Dieter Kratsch·Daniël Paulusma
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Abstract

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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Manfred Cochefert, Jean-François Couturier, Petr A. Golovach, Dieter Kratsch, Daniël Paulusma. 2013-10-21. Parameterized Algorithms for Finding Square Roots. https://arxiv.org/abs/1310.5469

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