Triangulability of convex graphs and convex skewness

Abstract

Suppose [Formula: see text] is a subgraph of a convex complete graph [Formula: see text] and [Formula: see text] contains no boundary edge of [Formula: see text] and [Formula: see text]. We determine necessary and sufficient conditions on [Formula: see text] such that [Formula: see text] admits a triangulation. For [Formula: see text], we investigate the possibility of placing [Formula: see text] in [Formula: see text] such that [Formula: see text] admits a triangulation for certain families of graphs [Formula: see text]. These results are then applied to determine the convex skewness of the convex graphs of the form [Formula: see text].