A Note on the Edge Reconstruction Conjecture

Abstract

We proved that if a graph $G$ of minimum valency $\delta =6\alpha +5$, with $\alpha$ a non-negative integer, can triangulate a surface $\mathrm{\Sigma }$ with $\chi (\mathrm{\Sigma })=-\alpha n+\beta$, where $\beta \in \{0,1,2\}$, then $G$ is edge reconstructible.