  There exists a Lipschitz embedding of a d-dimensional comb graph (consisting
of infinitely many parallel copies of Z^{d-1} joined by a perpendicular copy)
into the open set of site percolation on Z^d, whenever the parameter p is close
enough to 1 or the Lipschitz constant is sufficiently large. This is proved
using several new results and techniques involving stochastic domination, in
contexts that include a process of independent overlapping intervals on Z, and
first-passage percolation on general graphs.
