On the Edge Reconstruction of Graphs Embedded in Surfaces, III

In this paper, we prove that if a connected graphGembeddable in a surfaceΣof characteristicχ(Σ) satisfies (1) the minimum degree ofG⩾5, (2) |V(G)|⩾−43χ(Σ), thenGis edge reconstructible. A direct consequence of the above result is that a triangulationGof a surface of characteristicχ(Σ) is edge reconstructible if |V(G)|⩾−43χ(Σ).