AI 中文总结
研究关于三次和次三次图的零强制与独立数猜想，通过构造特定连通图作为反例，表明Z <= alpha + 1不是连通三次图通用界，且存在Z = alpha + 2的情况，反驳了相关猜想。
AI 中文摘要
我们展示了一个有24个顶点、最大度为3、独立数为9且零强制数为11的连通图，反驳了TxGraffiti在2017年的一个猜想（该猜想被记录为Davila、Brimkov和Pepper调查中的猜想2）。相同构造搭配不同小装置可得到一个有36个顶点、独立数为15且零强制数为17的连通三次图。所以该猜想在三次图形式下也不成立，即Z <= alpha + 1不是连通三次图的通用界，且达到了Z = alpha + 2的值。
英文摘要
We exhibit a connected graph on 24 vertices with maximum degree 3, independence number 9 and zero forcing number 11, refuting a 2017 conjecture of TxGraffiti recorded as Conjecture 2 of the survey of Davila, Brimkov and Pepper. The same construction with a different gadget gives a connected cubic graph on 36 vertices with independence number 15 and zero forcing number 17; the conjecture therefore fails also in the cubic form in which the survey's Lean 4 appendix states it. In particular Z <= alpha + 1 is not a universal bound for connected cubic graphs, and the value Z = alpha + 2 is attained.
Comments3 pages, 1 figure. Ancillary files include both counterexamples in graph6 format and a standalone Python script that verifies every claim in the note
