Two kernelization methods for the vertex cover problem are investigated. The first, LP-kernelization, has been in prior use and is known to produce predictable results. The second, crown reduction, is newer and faster but generates more variable results. Previously-unknown connections between these powerful methods are established. It is also shown that the problem of finding an induced crown-free subgraph in an ar-bitrary graph is decidable in polynomial time. Applications of crown structures are discussed.
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