AI 中文总结
该研究证明截角八面体图的束缚数为5，其为平面图且三次图，打破了非平凡平面图束缚数不超过最大度加1的猜想，通过穷举验证等方法完成结果核验。
AI 中文摘要
对于图G，其束缚数b(G)是删除后会增大其控制数的最少边数。Dunbar、Haynes、Teschner和Volkmann在1998年提出猜想：所有非平凡平面图都满足b(G)≤Δ(G)+1。本文证明截角八面体图T的控制数γ(T)=8，束缚数b(T)=5。由于T是平面图且为三次图，故b(T)=5>4=Δ(T)+1，该结果可推翻上述猜想。验证的有限部分为穷举性的：直接验证程序检查大小为6、7、8的候选控制集，以及全部58905个四元边集。文中还描述了定向发现搜索和独立编写的验证程序，完整的C++20验证程序包含在源文件压缩包中。
英文摘要
For a graph G, its bondage number b(G) is the minimum number of edges whose deletion increases its domination number. Dunbar, Haynes, Teschner, and Volkmann conjectured in 1998 that every nontrivial planar graph satisfies b(G) <= Delta(G) + 1. We show that the truncated octahedral graph T has gamma(T) = 8 and b(T) = 5. Since T is planar and cubic, this gives b(T) = 5 > 4 = Delta(T) + 1 and disproves the conjecture. The finite parts of the verification are exhaustive: the direct verifier checks candidate dominating sets of sizes six, seven, and eight and all 58,905 four-edge sets. The targeted discovery search and an independently written verifier are described, and the complete C++20 verifier is included in the source archive.
Comments5 pages, 1 figure; complete C++20 verifier and independent Python verifier included in the source archive
