Square roots of nearly planar graphs
Zden\v{e}k Dvo\v{r}\'ak, Benjamin Moore, Abhiruk Lahiri
TL;DR
This paper proves that determining whether a graph is the square of a 6-apex graph is NP-hard, indicating the computational difficulty of the square root problem for certain sparse graph classes.
Contribution
It establishes NP-hardness of recognizing squares of 6-apex graphs, highlighting the complexity of the square root problem for sparse and minor-closed graph classes.
Findings
NP-hardness of recognizing squares of 6-apex graphs
Square root problem is intractable for sparse graphs
Complexity persists even in minor-closed graph classes
Abstract
We prove that it is NP-hard to decide whether a graph is the square of a 6-apex graph. This shows that the square root problem is not tractable for squares of sparse graphs (or even graphs from proper minor-closed classes).
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Taxonomy
TopicsAdvanced Graph Theory Research · Computational Geometry and Mesh Generation · graph theory and CDMA systems