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Finding Cactus Roots in Polynomial Time.

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Area of Science:

  • Graph theory
  • Computational complexity

Background:

  • The Square Root problem involves determining if a graph G is the square of another graph H.
  • This is equivalent to checking if G can be formed from H by connecting vertices at distance 2.

Purpose of the Study:

  • To investigate the computational complexity of the Square Root problem.
  • To analyze the parameterized complexity of the Square Root problem with respect to specific graph classes.

Main Methods:

  • Demonstrating boundedness of treewidth for certain graph classes.
  • Algorithmic analysis of graph properties.

Main Results:

  • The Square Root problem is solvable in polynomial time for graphs with small clique numbers.
  • The parameterized Square Root problem is solvable in polynomial time when the target class is cactuses.

Conclusions:

  • The Square Root problem's complexity varies significantly depending on graph properties and specified classes.
  • Efficient algorithms exist for specific instances of the Square Root problem, particularly involving cactuses.