On asymptotic packing of convex geometric and ordered graphs
Jiaxi Nie, Erlang Surya, Ji Zeng

TL;DR
This paper establishes conditions under which convex geometric and ordered graphs can be packed into complete graphs, showing that graphs with certain chromatic numbers are always packable and identifying classes with many long edges that are also packable.
Contribution
It proves that convex geometric graphs with cyclic chromatic number at most 4 and ordered graphs with interval chromatic number at most 3 are always packable, extending understanding of graph packing.
Findings
Convex geometric graphs with cyclic chromatic number ≤ 4 are packable.
Ordered graphs with interval chromatic number ≤ 3 are packable.
Graphs with many long edges are also shown to be packable.
Abstract
A 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 is packable. With a similar definition of packability for ordered graphs, we prove that every ordered graph with interval chromatic number at most 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.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · Limits and Structures in Graph Theory
