A note on Erdős-Diophantine graphs and Diophantine carpets

Simple item page
dc.creatorKohnert, Axel
dc.creatorKurz, Sascha
dc.date2005-11-29
dc.date.accessioned2026-07-07T06:51:52Z
dc.date.available2026-07-07T06:51:52Z
dc.descriptionA Diophantine figure is a set of points on the integer grid $\mathbb{Z}^{2}$ where all mutual Euclidean distances are integers. We also speak of Diophantine graphs. In this language a Diophantine figure is a complete Diophantine graph. Due to a famous theorem of Erdős and Anning there are complete Diophantine graphs which are not contained in larger ones. We call them Erdős-Diophantine graphs. A special class of Diophantine graphs are Diophantine carpets. These are planar triangulations of a subset of the integer grid. We give an effective construction for Erdős-Diophantine graphs and characterize the chromatic number of Diophantine carpets.
dc.description4 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/math/0511705
dc.identifierhttp://arxiv.org/abs/math/0511705
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/105129
dc.subjectCombinatorics
dc.subject52C99
dc.titleA note on Erdős-Diophantine graphs and Diophantine carpets
dc.typetext

Files

Collections

arXiv