On the Edge Reconstruction of Graphs Embedded in Surfaces II
Yue Zhao · Journal of the London Mathematical Society · 1998
In this paper, we prove the following theorems. (i) Let G be a graph of minimum degree δ⩾5. If G is embeddable in a surface σ and satisfies (δ−5)∣V(G)∣+6χ(Σ)⩾0, then G is edge reconstructible. (ii) Any graph of minimum degree 4 that triangulates a surface is edge reconstructible. (iii) Any graph which triangulates a surface of characteristic χ⩾0 is edge reconstructible.