A Mathematical Proof of the Four-Color Conjecture (1): Transformation Step
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914674648285184 |
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| author | Xu, Jin |
| author_facet | Xu, Jin |
| contents | The four-color conjecture has puzzled mathematicians for over 170 years and has yet to be proven by purely mathematical methods. This series of articles provides a purely mathematical proof of the four-color conjecture, consisting of two parts: the transformation step and the decycle step. The transformation step uses two innovative tools, contracting and extending operations and unchanged bichromatic cycles, to transform the proof of the four-color conjecture into the decycle problem of 4-base modules. Moreover, the decycle step solves the decycle problem of 4-base modules using two other innovative tools: the color-connected potential and the pocket operations. This article presents the proof of the transformation step. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07361 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Mathematical Proof of the Four-Color Conjecture (1): Transformation Step Xu, Jin General Mathematics The four-color conjecture has puzzled mathematicians for over 170 years and has yet to be proven by purely mathematical methods. This series of articles provides a purely mathematical proof of the four-color conjecture, consisting of two parts: the transformation step and the decycle step. The transformation step uses two innovative tools, contracting and extending operations and unchanged bichromatic cycles, to transform the proof of the four-color conjecture into the decycle problem of 4-base modules. Moreover, the decycle step solves the decycle problem of 4-base modules using two other innovative tools: the color-connected potential and the pocket operations. This article presents the proof of the transformation step. |
| title | A Mathematical Proof of the Four-Color Conjecture (1): Transformation Step |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2402.07361 |