On asymptotic packing of geometric graphs

A set of geometric graphs is geometric-packable if it can be asymptotically packed into every sequence drawings the complete graph Kn. For example, triangles due to existence Steiner Triple Systems. When G 4-cycle (or with a chord), we show that plane geometric-packable. In contrast, analogous statement false when nearly any other planar Hamiltonian (with at most 3 possible exceptions). convex convex-packable graphs. each G, determine whether or not convex-packable. Many our proofs explicitly construct these packings; in cases, packings exhibit symmetry mirrors vertex transitivity