Forbidden k‐Sets in the Plane

Abstract

Let $A$ be a set of nonnegative integers. We say that $A$ is skippable if there are arbitrary large finite sets of points in the plane, not contained in a line, that determine no $k$-edge for any $k \in A$. In this paper we show, by construction, that there are arbitrary large skippable sets. We also characterize precisely the skippable sets with at most two elements.