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• W2624596731 abstract "We show that every triangulation (maximal planar graph) on n≥6 vertices can be flipped into a Hamiltonian triangulation using a sequence of less than n/2 combinatorial edge flips. The previously best upper bound uses 4-connectivity as a means to establish Hamiltonicity. But in general about 3n/5 flips are necessary to reach a 4-connected triangulation. Our result improves the upper bound on the diameter of the flip graph of combinatorial triangulations on n vertices from 5.2n−33.6 to 5n−23. We also show that for every triangulation on n vertices there is a simultaneous flip of less than 2n/3 edges to a 4-connected triangulation. The bound on the number of edges is tight, up to an additive constant. As another application we show that every planar graph on n vertices admits an arc diagram with less than n/2 biarcs, that is, after subdividing less than n/2 (of potentially 3n−6) edges the resulting graph admits a 2-page book embedding." @default.
• W2624596731 created "2017-06-15" @default.
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• W2624596731 date "2018-03-01" @default.
• W2624596731 modified "2023-10-17" @default.
• W2624596731 title "Arc diagrams, flip distances, and Hamiltonian triangulations" @default.
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• W2624596731 doi "https://doi.org/10.1016/j.comgeo.2017.06.001" @default.
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