Ignition of combustible boundary-layer flows over a hot wedge in a gravitational field is investigated theoretically by the method of large activation energy asymptotics. The problem of interest is intrinsically non-similar and non-symmetric even for stagnation-point flows. An explicit ignition criterion as a function of all relevant system parameters is obtained. A comparison between ignition phenomena under mixed convection and those under pure forced convection is systematically made. For small wedge angles (nearly horizontal boundary-layer flows), under mixed convection the results of ignition distances for the upper and the lower boundary-layer flows are distinct qualitatively and quantitatively. For the stagnation-point flow, ignition phenomena are highly sensitive to the buoyancy force. The ignition of stagnation-point flows under mixed convection exhibits a totally non-symmetrical configuration. The wedge angles and the wall temperatures at the transition of ignition regions are different for the upper and the lower boundary-layer flows. For wedge angles greater than pi, ignition behaviors under mixed convection are qualitatively consistent with those under pure forced convection due to sufficiently great flow accelerations.