On asymptotic packing of convex geometric and ordered graphs

Abstract

AbstractA convex geometric graph is said to be packable if there exist edge‐disjoint copies of in the complete convex geometric graph covering all but 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 the best possible. We also identify a class of convex geometric graphs that are packable due to having many “long” edges.