  The 3-\textsc{Hitting Set} problem is also called the \textsc{Vertex Cover}
problem on 3-uniform hypergraphs. In this paper, we address kernelizations of
the \textsc{Vertex Cover} problem on 3-uniform hypergraphs. We show that this
problem admits a linear kernel in three classes of 3-uniform hypergraphs. We
also obtain lower and upper bounds on the kernel size for them by the
parametric duality.
