AI 中文总结
该研究确定四顶点蓝-蓝-红路径相关图论量的最大极限值，给出极值构造，用带权顶点商和度平方破局完成证明，解决了非完全红蓝图分类遗留的四顶点问题。
AI 中文摘要
对于n顶点图G，设N(H₃,G)为红蓝路径H₃的单射标记副本数，其中两个蓝对映射为G的非边，红对映射为G的边。我们确定N(H₃,G)/n⁴的最大极限值并给出极值构造，该构造是一个团与一个渐近正则图的不交并。证明使用带权顶点商和度平方破局，由此解决了近期非完全红蓝图分类中遗留的四顶点特殊情形。
英文摘要
For an $n$-vertex graph $G$, let $N(H_3,G)$ be the number of injective labeled copies of the red-blue path $H_3$ for which the two blue pairs are mapped to non-edges of $G$ and the red pair is mapped to an edge of $G$. We determine the maximum limiting value of $N(H_3,G)/n^4$ and give an extremal construction, which is the disjoint union of a clique and an asymptotically regular graph. The proof uses weighted vertex quotients and degree-square tie-breaking. We thereby resolve the exceptional four-vertex case left open in the recent classification of non-complete red-blue graphs.
