  Given $t$ distinct colors, we order the $t$ subsets of $t-1$ colors in some
arbitrary manner. Let $G_1, G_2, \ldots , G_t$ be graphs. The $(t-1)$-chromatic
Ramsey number, denoted by $r_{t-1}^t(G_1, G_2, \ldots, G_t)$, is defined to be
the least number $n$ such that if the edges of the complete graph $K_n$ are
colored in any fashion with $t$ colors, then for some $i$ the subgraph whose
edges are colored with the $i$th subset of colors contains a copy of $G_i$. In
this paper, we find the value of $r_{t-1}^t(G_1, G_2, \ldots, G_t)$ when each
$G_i$ is a path.
