  A colored link, as defined by Francesca Aicardi, is an oriented classical
link together with a coloration, which is a function defined on the set of link
components and whose image is a finite set of colors. An oriented classical
link can be regarded as a colored link with its components colored with a sole
color. Aicardi constructed an invariant $F(L)$ of colored links $L$ defined via
skein relations. When the components of a colored link are colored with the
same color or when the colored link is a knot, $F(L)$ is a specialization of
the HOMFLY-PT polynomial. Aicardi also showed that $F(L)$ is a stronger
invariant than the HOMFLY-PT polynomial when evaluated on colored links whose
components have different colors. In this paper, we provide a state-sum model
for the invariant $F(L)$ of colored links using a graphical calculus for
oriented, colored, 4-valent planar graphs. We also extend $F(L)$ to an
invariant of oriented colored singular links.
