  Ramsey's theorem states that each coloring has an infinite homogeneous set,
but these sets can be arbitrarily spread out. Paul Erdos and Fred Galvin proved
that for each coloring f, there is an infinite set that is "packed together"
which is given "a small number" of colors by f.
  We analyze the strength of this theorem from the perspective of computability
theory and reverse mathematics. We show that this theorem is close in
computational strength to standard Ramsey's theorem by giving arithmetical
upper and lower bounds for solutions to computable instances. In reverse
mathematics, we show that that this packed Ramsey's theorem is equivalent to
Ramsey's theorem for exponents not equal to 2. When n=2, we show that it
implies Ramsey's theorem, and that it does not imply ACA_0.
