Audet, Charles; Hansen, Pierre; Messine, Frédéric; Xiong, Junjie The largest small octagon. (English) Zbl 1022.90013 J. Comb. Theory, Ser. A 98, No. 1, 46-59 (2002). Summary: Thrackleation of graphs and global optimization for quadratically constrained quadratic programming are used to find the octagon with unit diameter and largest area. This proves the first open case of a conjecture of R. L. Graham [ibid. 18, 165-170 (1975; Zbl 0299.52006)]. Cited in 1 ReviewCited in 23 Documents MSC: 90C20 Quadratic programming 51-XX Geometry 52-XX Convex and discrete geometry Keywords:octagon; area; diameter; thrackleation; quadratic programming Citations:Zbl 0299.52006 PDFBibTeX XMLCite \textit{C. Audet} et al., J. Comb. Theory, Ser. A 98, No. 1, 46--59 (2002; Zbl 1022.90013) References: [1] Audet, C., Optimisation globale structurée: propriétés, équivalences et résolution (1997), École Polytechnique de Montréal [2] Audet, C.; Hansen, P.; Jaumard, B.; Savard, G., A branch and cut algorithm for nonconvex quadratically constrained quadratic programming, Math. Programming, 87, 131-152 (2000) · Zbl 0966.90057 [3] Graham, R. L., The largest small hexagon, J. Combin. Theory Ser. A, 18, 165-170 (1975) · Zbl 0299.52006 [4] Reinhardt, K., Extremale Polygone gegebenen Durchmessers, Jahresber. Deutsch. Math. Verein, 31, 251-270 (1922) [5] Woodall, D. R., Thrackles and deadlock, (Welsh, D. J.A, Combinatorial Mathematics and Its Applications (1971), Academic Press: Academic Press New York) · Zbl 0213.50603 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.