Triangulability of convex graphs and convex skewness
Abstract
Suppose F is a subgraph of a convex complete graph Kn and F contains no boundary edge of Kn and |E(F)|≤n−1. We determine necessary and sufficient conditions on F such that Kn−F admits a triangulation. For |E(F)|≥n, we investigate the possibility of placing F in Kn such that Kn−F admits a triangulation for certain families of graphs F. These results are then applied to determine the convex skewness of the convex graphs of the form Kn−F.
Communicated by Liying Kang
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