We have measured a strong increase of the low-temperature resistivity ${\ensuremath{\rho}}_{xx}$ and a zero-value plateau in the Hall conductivity ${\ensuremath{\sigma}}_{xy}$ at the charge neutrality point in graphene subjected to high magnetic fields up to 30 T. We explain our results by a simple model involving a field dependent splitting of the lowest Landau level of the order of a few Kelvin, as extracted from activated transport measurements. The model reproduces both the increase in ${\ensuremath{\rho}}_{xx}$ and the anomalous $\ensuremath{\nu}=0$ plateau in ${\ensuremath{\sigma}}_{xy}$ in terms of coexisting electrons and holes in the same split zero-energy Landau level.
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