Minimal Polynomials for the Coordinates of the Harborth Graph

dc.creatorGerbracht, Eberhard H. -A.
dc.date2006-09-13
dc.date2007-01-24
dc.date.accessioned2026-07-07T08:30:56Z
dc.date.available2026-07-07T08:30:56Z
dc.descriptionThe Harborth graph is the smallest known example of a 4-regular planar unit-distance graph. In this paper we give an analytical description of the coordinates of its vertices for a particular embedding in the Euclidean plane. More precisely, we show, how to calculate the minimal polynomials of the coordinates of its vertices (with the help of a computer algebra system), and list those. Furthermore some algebraic properties of these polynomials, and consequences to the structure of the Harborth graph are determined.
dc.descriptionv1: documentclass amsart, 16 pages, 4 figures. v2: same as v1, but now has 18 pages, with a final section ("Coda") on the consequences to the structure of the Harborth graph and some references added; some typos corrected. v3: minor change to the introduction (re: history of the Harborth Graph); one reference added; some more typos corrected
dc.identifierhttps://arxiv.org/abs/math/0609360
dc.identifierhttp://arxiv.org/abs/math/0609360
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/138372
dc.subjectCombinatorics
dc.subjectSymbolic Computation
dc.subject05C62 (Primary); 05C10, 13P10 (Secondary)
dc.titleMinimal Polynomials for the Coordinates of the Harborth Graph
dc.typetext

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