AI 中文总结
本研究通过穷举计算将Erdős-Gyárfás猜想的立方二分反例的顶点下界从30提升至60，验证了顶点数≤58的简单立方二分图必含4、8或16环，证明过程结合Moore界、Levi图转化与受限增长搜索，结果经多重方式验证。
AI 中文摘要
经过验证的穷举计算表明，每个顶点数不超过58的简单立方二分图都包含长度为4、8或16的环。因此，Erdős-Gyárfás猜想的任何立方二分反例至少有60个顶点，将该类反例已发表的既定下界从30提升至60。证明始于Moore界的观察：在62个顶点以下，不含4环和8环的立方二分图必含6环。将该图视为线性对称v3构型的Levi图，此6环便转化为Berge三角形。在对称意义下，仅存在两种有根扩展可能。对最多29个点进行的完整受限增长搜索穷尽了两棵搜索树。该计算通过两个分别采用不同C16预言机实现的独立精确程序，以及一个静态见证证书进行了验证。源代码、证书和复现说明随论文存档。
英文摘要
A certified exhaustive computation shows that every simple cubic bipartite graph on at most 58 vertices contains a cycle of length 4, 8, or 16. Consequently, any cubic bipartite counterexample to the Erdos-Gyarfas conjecture has at least 60 vertices, improving the established published lower bound for this class from 30 to 60. The proof begins with a Moore-bound observation: below 62 vertices, a cubic bipartite graph avoiding 4- and 8-cycles must contain a 6-cycle. Viewing the graph as the Levi graph of a linear symmetric v3-configuration turns this 6-cycle into a Berge triangle. Up to symmetry, only two rooted extensions are possible. A complete restricted-growth search on at most 29 points exhausts both search trees. The computation is checked by two separately implemented exact procedures using different C16 oracles and by a static witness certificate. Source code, certificates, and reproduction instructions are archived with the paper.
Comments19 pages. 4 figures. Computer-assisted proof with complete source code, witness certificates, and reproducibility artifact available from the accompanying GitHub repository and Zenodo archive
