Happy endings for flip graphs
<|reference_start|>Happy endings for flip graphs: We show that the triangulations of a finite point set form a flip graph that can be embedded isometrically into a hypercube, if and only if the point set has no empty convex pentagon. Point sets of this type include convex subsets of lattices, points on two lines, and several other infinite families. As a consequence, flip distance in such point sets can be computed efficiently.<|reference_end|>
@article{eppstein2006happy,
    title={Happy endings for flip graphs},
    author={David Eppstein},
    journal={Journal of Computational Geometry 1(1):3-28, 2010},
    year={2006},
    doi={10.20382/jocg.v1i1a2},
    archivePrefix={arXiv},
    eprint={cs/0610092},
    primaryClass={cs.CG math.CO math.MG}
}