Heule 图是由 Marijn Heule 于 2018 年 4 月至 2918 年 7 月从 1581 个顶点的 de Grey 图 (Heule 2018) 推导出来的一组单位距离图，其色数为 5。它们提供了一些已知的最小例子，这些例子确定了Hadwiger-Nelson 问题（即平面的色数）的解为 5、6 或 7。这个 529 个顶点的图是在大约 100,000 CPU 小时的计算后发现的 (Heule 2019)。
Jaan Parts 发现了其他小型图，并在本文中称为 Parts 图。
Heule 图示于上方，并在下表中进行了总结。
| 顶点计数 | 边计数 | 发现日期 |
| 874 | 4461 | Apr. 14, 2018 |
| 826 | 4273 | Apr. 16, 2018 |
| 803 | 4144 | Apr. 30, 2018 |
| 633 | 3166 | May 6, 2018 |
| 610 | 3000 | May 14, 2018 |
| 553 | 2722 | May 30, 2018 |
| 529 | 2670 | Jul. 1, 2019 |
| 517 | 2579 | Jul. 28, 2019 |
| 510 | 2504 | Aug. 8, 2019 |
Heule 图在 Wolfram Language 中实现为GraphData["HeuleGraph510"] 等。
参见
de Grey 图、
Hadwiger-Nelson 问题、
Heule 纺锤、
Mixon 图、
Parts 图、
单位距离图
使用 Wolfram|Alpha 探索
参考文献
de Grey, A. D. N. J. "The Chromatic Number of the Plane Is at Least 5." Geombinatorics 28, No. 1, 18-31, 2018.Heule, M. May 6, 2018. https://dustingmixon.wordpress.com/2018/05/05/polymath16-fourth-thread-applying-the-probabilistic-method/#comment-4316.Heule, M. May 14, 2018. https://dustingmixon.wordpress.com/2018/05/10/polymath16-fifth-thread-human-verifiable-proofs/#comment-4465.Heule, M. J. H. "Computing Small Unit-Distance Graphs with Chromatic Number 5." Geombinatorics 28, 32-50, 2018.Heule, M. "Computing Small Unit-Distance Graphs with Chromatic Number 5." 30 May 2018. https://arxiv.org/abs/1805.12181.Heule, M. "Computing a Smaller Unit-Distance Graph with Chromatic Number 5 via Proof Trimming." 1 Jul 2019. https://arxiv.org/abs/1907.00929.Lamb, E. "Decades-Old Graph Problem Yields to Amateur Mathematician." Quanta Mag. Apr. 17, 2018. https://www.quantamagazine.org/decades-old-graph-problem-yields-to-amateur-mathematician-20180417/.Mixon, D. G. "Polymath16, First Thread: Simplifying De Grey's Graph." 14 Apr 2018. https://dustingmixon.wordpress.com/2018/04/14/polymath16-first-thread-simplifying-de-greys-graph/.Parts, J. "Graph Minimization, Focusing on the Example of 5-Chromatic Unit-Distance Graphs in the Plane." Geombinatorics 29, No. 4, 137-166, 2020.PolyMath. "Hadwiger-Nelson Problem." http://michaelnielsen.org/polymath1/index.php?title=Hadwiger-Nelson_problem.Soifer, A. "Marienus Johannes Hendrikus 'Marijn' Heule." Ch. 53 in The New Mathematical Coloring Book: Mathematics of Coloring and the Colorful Life of Its Creators, 2nd ed. New York: Springer, pp. 675-692, 2024.
请引用为
Weisstein, Eric W. "Heule 图。" 来自 MathWorld--Wolfram Web 资源。 https://mathworld.net.cn/HeuleGraphs.html
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