AI 中文总结
针对Hadwiger-Nelson问题，本研究构造出不含Moser纺锤体的2131顶点5色单位距离图，改进了此前64513顶点的同类结果，利用21顶点7对称单位距离图的弧完成构造。
AI 中文摘要
关于Hadwiger-Nelson问题，近年来已发现欧几里得平面上多个5色单位距离图。多数构造严重依赖Moser纺锤体，而Voronov等人找到了完全不含该结构的64513顶点示例。本研究改进了该结果，提出一个不含Moser纺锤体的2131顶点5色单位距离图，其构造利用了21顶点7对称单位距离图的弧。
英文摘要
With regard to the Hadwiger-Nelson problem, several 5-chromatic unit distance graphs in the Euclidean plane have been discovered in recent years. While most constructions rely heavily on the Moser spindle, a few recent examples completely avoid it, the smallest one consisting of 1441 vertices. In this note, we introduce an original geometric approach to constructing such graphs by utilizing the arcs of a 7-fold symmetric unit distance graph on 21 vertices, and obtain a Moser-spindle-free 5-chromatic unit distance graph on 2131 vertices. While this is not a record small result, it arises from a straightforward, structured rule rather than a purely automated or brute-force search.
Comments9 pages, 2 figures. Added links to preprints with recent developments. Added AI use declaration. Corrected page numbers in one reference
