On asymptotic packing of convex geometric and ordered graphs

Abstract

A convex geometric graph G is said to be packable if there exist edge-disjoint copies of G in the complete convex geometric graph K n covering all but o(n 2 ) edges. We prove that every convex geometric graph with cyclic chromatic number at most 4 is packable. With a similar definition of packability for ordered graphs, we prove that every ordered graph with interval chromatic number at most 3 is packable. Arguments based on the average length of edges imply these results are best possible. We also identify a class of convex geometric graphs that are packable due to having many "long" edges.