  For any c >= 2, a c-strong coloring of the hypergraph G is an assignment of
colors to the vertices of G such that for every edge e of G, the vertices of e
are colored by at least min{c,|e|} distinct colors. The hypergraph G is
t-intersecting if every two edges of G have at least t vertices in common. We
ask: for fixed c >= 2 and t >= 1, what is the minimum number of colors that is
sufficient to c-strong color any t-intersecting hypergraphs?
  The purpose of this note is to answer the question for some values of t and c
and, more importantly, to describe the settings for which the question is still
open. We show that when t <= c-2, no finite number of colors is sufficient to
c-strong color all t-intersecting hypergraphs. It is still unknown whether a
finite number of colors suffices for the same task when t = c-1 and c > 2. In
the last case, when t >= c, we show with a probabilistic argument that a finite
number of colors is sufficient to c-strong color all t-intersecting
hypergraphs, but a large gap still remains between the best upper and lower
bounds on this number.
