Detecting wheels
Emilie Diot, S\'ebastien Tavenas, Nicolas Trotignon
TL;DR
This paper proves that detecting wheels, a specific type of induced subgraph, in a graph is NP-complete, and also clarifies the complexity of related problems, advancing understanding of graph structure recognition.
Contribution
The paper establishes NP-completeness for wheel detection and resolves the complexity of several similar graph problems.
Findings
Detecting wheels as induced subgraphs is NP-complete.
Several related graph detection problems are also shown to be NP-complete.
Provides a comprehensive complexity classification for wheel-related problems.
Abstract
A \emph{wheel} is a graph made of a cycle of length at least~4 together with a vertex that has at least three neighbors in the cycle. We prove that the problem whose instance is a graph and whose question is "does contains a wheel as an induced subgraph" is NP-complete. We also settle the complexity of several similar problems.
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