A Forced-Structure Reduction and Verifiable Bounds for Conway's 99-Graph
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Conway's 99-GraphVerifiable BoundsForced-Structure ReductiCAISc Constraints
该研究通过结构约束和验证边界方法，缩小了Conway 99图存在的搜索空间，验证了部分构造并提升了验证得分。
This paper reduces the search space for Conway's 99-graph problem using structural constraints and verifiable bounds, achieving higher verified partial constructions.
Key points
- 通过固定顶点条件，将问题转化为约束12正则图的验证 Reduces the problem to a constrained 12-regular graph via vertex fixing
- 穷举证明循环图无法满足超过68%的约束条件 Proves circulant graphs meet <68% of CAISc constraints
- 进化算法生成的4顶点交换搜索获得70.73%验证得分 Evolutionary search achieves 70.73% verified score
- 提出可验证轨道公式用于指定自同构 Provides verifiable orbit formulation for automorphisms
Takeaway: 结构约束与验证方法为复杂图问题提供了新解题思路 / Structural constraints and verification offer new approaches for complex graph problems
Why it matters 为复杂图问题的验证性搜索提供了可操作的框架与量化指标
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