Probabilistic Counting Proof of the Four-Color Conjecture
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2026
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| _version_ | 1866901456932569088 |
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| author | Wang, Jude |
| author_facet | Wang, Jude |
| contents | <p><span>本文提出一种基于</span><strong><span>概率计数与极限分析</span></strong><span>的四色猜想证明方法。通过将问题等价转化为极大平面图的</span><span>4可着色性问题,引入概率上界引理</span><span>,结合极大平面图的已知计数结果,证明当顶点数</span> <span>n 足够大时,不可4着色的极大平面图(反例)个数 R(n) = 0;对较小 n 逐一验证后,最终得到所有 n≥4 的极大平面图均为4可着色,从而完成四色猜想的证明。</span></p> <p><span>In this paper, we propose a proof method for the four-color conjecture based on probabilistic counting and limit analysis. By equivalently transforming the problem into the 4-colorability problem of maximal planar graphs, we introduce a probabilistic upper bound lemma and combine known counting results for maximal planar graphs to prove that the number R(n) of non-4-colorable maximal planar graphs (counterexamples) is equal to 0 when the number of vertices n is sufficiently large. After verifying all small values of n one by one, we conclude that all maximal planar graphs with n≥4 are 4-colorable, thus completing the proof of the four-color conjecture.</span></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19397106 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Probabilistic Counting Proof of the Four-Color Conjecture Wang, Jude <p><span>本文提出一种基于</span><strong><span>概率计数与极限分析</span></strong><span>的四色猜想证明方法。通过将问题等价转化为极大平面图的</span><span>4可着色性问题,引入概率上界引理</span><span>,结合极大平面图的已知计数结果,证明当顶点数</span> <span>n 足够大时,不可4着色的极大平面图(反例)个数 R(n) = 0;对较小 n 逐一验证后,最终得到所有 n≥4 的极大平面图均为4可着色,从而完成四色猜想的证明。</span></p> <p><span>In this paper, we propose a proof method for the four-color conjecture based on probabilistic counting and limit analysis. By equivalently transforming the problem into the 4-colorability problem of maximal planar graphs, we introduce a probabilistic upper bound lemma and combine known counting results for maximal planar graphs to prove that the number R(n) of non-4-colorable maximal planar graphs (counterexamples) is equal to 0 when the number of vertices n is sufficiently large. After verifying all small values of n one by one, we conclude that all maximal planar graphs with n≥4 are 4-colorable, thus completing the proof of the four-color conjecture.</span></p> |
| title | Probabilistic Counting Proof of the Four-Color Conjecture |
| url | https://doi.org/10.5281/zenodo.19397106 |