Beta-skeletons have unbounded dilation (Q1614068)

A number of authors have studied the question of dilation of various geometric graphs [see \textit{D. Eppstein} in: Handbook of computational geometry, Chapter 9, 425-461 (2000; Zbl 0544.05021)]. The author studies here beta-skeletons [cf. \textit{R. C. Veltkamp}, Comput. Geom. 1, No.~4, 227-246 (1992; Zbl 0748.68089)], which are of more recent interest. It is shown here that one can find point sets for which the beta-skeleton has arbitrarily high dilation. The construction given here uses fractal curves closely related to Koch snowflake.