  A $(a,b)$-coloring of a graph $G$ associates to each vertex a $b$-subset of a
set of $a$ colors in such a way that the color-sets of adjacent vertices are
disjoint. We define general reduction tools for $(a,b)$-coloring of graphs for
$2\le a/b\le 3$. In particular, using necessary and sufficient conditions for
the existence of a $(a,b)$-coloring of a path with prescribed color-sets on its
end-vertices, more complex $(a,b)$-colorability reductions are presented. The
utility of these tools is exemplified on finite triangle-free induced subgraphs
of the triangular lattice for which McDiarmid-Reed's conjecture asserts that
they are all $(9,4)$-colorable. Computations on millions of such graphs
generated randomly show that our tools allow to find a $(9,4)$-coloring for
each of them except for one specific regular shape of graphs (that can be
$(9,4)$-colored by an easy ad-hoc process). We thus obtain computational
evidence towards the conjecture of McDiarmid\&Reed.
