  We introduce the concept of edgewise domination in clutters, and use it to
provide an upper bound for the projective dimension of any squarefree monomial
ideal. We then use a simple recursion to recover a formula for the projective
dimension of a monomial ideal associated to a chordal clutter, as defined by
Woodroofe in \cite{russ}. We also study a family of clutters associated to
graphs, and show that these clutters are chordal if and only if the associated
graph is. Finally, we compute domination parameters for certain classes of
these clutters.
