Partitions of Complete Bipartite Geometric Graphs Into Plane Perfect Matchings

Trao, Hazim Michman; Chia, G. L.; Ali, Niran Abbas; Kılıçman, Adem

doi:10.17654/ms110010041

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2023

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“…To end this introduction, we remark that research has been done for packing problems of (not necessarily convex) geometric graphs [1, 4–6, 15, 20]. The extremal problems about cgg's and ordered graphs are also extensively studied, with many results particularly related to cyclic chromatic numbers and/or interval chromatic numbers [3, 7, 9, 11, 16].…”

Section: Introductionmentioning

confidence: 99%

On asymptotic packing of convex geometric and ordered graphs

Nie

Erlang

Zeng

2023

Journal of Graph Theory

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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 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.

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Section: Introductionmentioning

confidence: 99%