  In the present work we investigate the cosmological implications of
holographic dark energy density in the Gauss-Bonnet framework. By formulating
independently the two cosmological scenarios, and by enforcing their
simultaneous validity, we show that there is a correspondence between the
holographic dark energy scenario in flat universe and the phantom dark energy
model in the framework of Gauss-Bonnet theory with a potential. This
correspondence leads consistently to an accelerating universe. However, in
general one has not full freedom of constructing independently the two
cosmological scenarios. Specific constraints must be imposed on the coupling
with gravity and on the potential.
