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Finding Cactus Roots in Polynomial Time
Petr A Golovach1, Dieter Kratsch2, Daniël Paulusma3
11Department of Informatics, University of Bergen, PB 7803, 5020 Bergen, Norway.
This study explores the graph Square Root problem, determining if a graph has a square root. Researchers show the problem is efficiently solvable for certain graphs and specific classes like cactuses.
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.
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