In this paper, two sufficient conditions for identifying a subgraph of
minimum weight triangulation of a planar point set are presented. The
se conditions are based on local geometric properties of an edge to be
identified. Unlike the previous known sufficient conditions for ident
ifying subgraphs, such as Keil's beta-skeleton and Yang and Xu's doubl
e circles, The local geometric requirement in our conditions is not ne
cessary symmetric with respect to the edge to be identified. The ident
ified subgraph is different from all the known subgraphs including the
newly discovered subgraph: so-called the intersection of local-optima
l triangulations by Dickerson et al. An O(n(3)) time algorithm for fin
ding this subgraph from a set of n points is presented.