Heule 圖是由 Marijn Heule 於 2018 年 4 月至 2918 年 7 月從 1581 個頂點的 de Grey 圖 (Heule 2018) 推匯出來的一組單位距離圖，其色數為 5。它們提供了一些已知的最小例子，這些例子確定了Hadwiger-Nelson 問題（即平面的色數）的解為 5、6 或 7。這個 529 個頂點的圖是在大約 100,000 CPU 小時的計算後發現的 (Heule 2019)。
Jaan Parts 發現了其他小型圖，並在本文中稱為 Parts 圖。
Heule 圖示於上方，並在下表中進行了總結。
| 頂點計數 | 邊計數 | 發現日期 |
| 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 圖在 Wolfram Language 中實現為GraphData["HeuleGraph510"] 等。
參見
de Grey 圖、
Hadwiger-Nelson 問題、
Heule 紡錘、
Mixon 圖、
Parts 圖、
單位距離圖
使用 探索
參考文獻
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.
請引用為
Weisstein, Eric W. "Heule 圖。" 來自 Web 資源。 https://mathworld.tw/HeuleGraphs.html
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