Two discrete versions of the Inscribed Square Conjecture and some related problems

@article{Sagols2011TwoDV,
title={Two discrete versions of the Inscribed Square Conjecture and some related problems},
author={F. Sagols and Ra{\'u}l Mar{\'i}n},
journal={Theor. Comput. Sci.},
year={2011},
volume={412},
pages={1301-1312}
}

The Inscribed Square Conjecture has been open since 1911. It states that any plane Jordan curve J contains four points on a non-degenerate square. In this article two different discrete versions of this conjecture are introduced and proved. The first version is in the field of digital topology: it is proved that the conjecture holds for digital simple closed 4-curves, and that it is false for 8-curves. The second one is in the topological graph theory field: it is proved that any cycle of the… Expand