  We study a holographic model of quantum chromodynamics, which can describe a
color superconductor and a dilute nucleon gas phase. The two phases are
adjoined in the phase diagram at a critical value of the chemical potential. In
other words, a first-order transition from the ordinary nucleon gas to the
color superconductor is found by increasing the chemical potential. This model
is suitable to investigate the possibility of a cold compact star with a color
superconducting core. The equation of state of the star is given by the
holographic model considered in this article, and we find that it is impossible
in the present model to find a hybrid star of nuclear matter and the color
superconductor core through the relation of mass and radius of the star by
solving the Tolman-Oppenheimer-Volkoff equations. Several other interesting
implications are given by using the equation of state.
