Graphs associated with triangulations of lattice polygons

Two graphs, the edge crossing graph E and the triangle graph T are associated with a simple lattice polygon. The maximal independent sets of vertices of E and T correspond to the triangulations of the polygon into fundamental triangles. Properties of E and T are derived including a formula for the size of the maximal independent sets in E and T. It is shown that T is a factor graph of edge-disjoint 4-cycles, which gives corresponding geometric information, and is a partition graph as recently defined by the authors and F. Harary. 1980 Mathematics subject classification (Amer. Math. Soc.) (1985 Revision): 05 C 99, 51 M 05, 52 A 43.