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Let $c\phi_{k}(n)$ be the number of $k$-colored generalized Frobeniuspartitions of $n$. We establish some infinite families of congruences for$c\phi_{3}(n)$ and $c\phi_{9}(n)$ modulo arbitrary powers of 3, which refinethe results of Kolitsch. For example, for $k\ge 3$ and $n\ge 0$, we prove that\[c\phi_{3}\Big(3^{2k}n+\frac{7\cdot 3^{2k}+1}{8}\Big) \equiv 0\pmod{3^{4k+5}}.\] We give two different proofs to the congruences satisfied by$c\phi_{9}(n)$. One of the proofs uses an relation between $c\phi_{9}(n)$ and$c\phi_{3}(n)$ due to Kolitsch, for which we provide a new proof in this paper.

Congruences Modulo Powers of 3 for 3- and 9-Colored Generalized Frobenius Partitions