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Harborth 图

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HarborthGraph

Harborth 图是已知的最小的 4-正则 火柴棍图。因此，它既是平面的，也是单位距离的。它有 104 条边和 52 个顶点。这个图以其发现者 H. Harborth 的名字命名，他于 1986 年首次向公众展示了它（Harborth 1994, Petersen 1996, Gerbracht 2006, Winkler等人 2017）。

Harborth 图在 Wolfram 语言中实现为GraphData["HarborthGraph"].

Gerbracht (2006) 推导出了由 22 次代数数（具有大系数）组成的顶点的解析表达式。因此，Gerbracht (2006) 也证明了 Harborth 图是刚性的。

参见

火柴棍图, 正则图, 刚性图, 单位距离图

使用 Wolfram|Alpha 探索

参考文献

Bode, J.-P.; Harborth, H.; and Thürmann, C. "Minimum Regular Rectilinear Plane Graph Drawings with Fixed Numbers of Edge Lengths." Congr. Numer. 169, 193-198, 2004.Gerbracht, E. H.-A. "Minimal Polynomials for the Coordinates of the Harborth Graph." Oct. 5, 2006. http://arxiv.org/abs/math.CO/0609360.Harborth, H. "Match Sticks in the Plane." In The Lighter Side of Mathematics. Proceedings of the Eugéne Strens Memorial Conference of Recreational Mathematics & its History. Calgary, Canada, July 27-August 2, 1986 (Eds. R. K. Guy and R. E. Woodrow). Washington, DC: Math. Assoc. Amer., pp. 281-288, 1994.Harborth, H. and Kemnitz, A. "Integral Representations of Graphs." In Contemporary Methods in Graph Theory (Ed. R. Bodendiek). Mannheim, Germany: B.I.-Wissenschaftsverlag, pp. 359-367, 1990.Hartsfield, N. and Ringel, G. Pearls in Graph Theory: A Comprehensive Introduction. San Diego, CA: Academic Press, 1990.Kurz, S. "No Finite 5-Regular Matchstick Graph Exists." 8 Jan 2014. https://arxiv.org/abs/1401.1793.Kurz, S. and Pinchasi, R. "Regular Matchstick Graphs." Amer. Math. Monthly 118, 264-267, 2011.Pegg, E. Jr. "Material added 8 Jan 06 (Happy New Year)." http://www.mathpuzzle.com/26Feb2006.html.Peterson, I. "Mathland: Matchsticks in the Summer." August 1996. http://www.sciencenews.org/pages/sn_arch/8_10_96/mathland.htm.Winkler, M.; Dinkelacker, P.; and Vogel, S. "New Minimal (4;n)-Regular Matchstick Graphs." Geocombinatorics 27, 26-44, Jul. 2017.

引用为

Weisstein, Eric W. "Harborth 图。" 来自 MathWorld--Wolfram 网络资源。 https://mathworld.net.cn/HarborthGraph.html

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