A strict connection tree of a graph G for a set W is a tree subgraph of G whose leaf set equals W. The Strict terminal connection problem (S-TCP) is a network design problem whose goal is to decide whether G admits a strict connection tree T for W with at most ℓ vertices of degree 2 and r vertices of degree at least 3. We establish a Poly vs. NP-c dichotomy for S-TCP with respect to ℓ and $\mathrm{\Delta }(G)$. We prove that S-TCP parameterized by r is $\text{W}[2]$-hard even if ℓ is bounded by a constant; we provide a kernelization for S-TCP parameterized by ℓ, r and $\mathrm{\Delta }(G)$, and we prove that such a version of the problem does not admit a polynomial kernel, unless $\text{NP}\subseteq \text{coNP/poly}$. Finally, we analyze S-TCP on split graphs and cographs.

的曲线图的严格连接树ģ一组W¯¯是树子图ģ其叶集等于w ^。在严格的终端连接问题（S-TCP）是一个网络设计问题，其目的是决定是否摹承认了严格的连接树牛逼的W¯¯最多有ℓ度为2的顶点，[R程度的顶点至少3.我们建立关于ℓ和S的Poly与NP-c二分法$\mathrm{\Delta }（G）$。我们证明由r参数化的S-TCP为$\text{w ^}[2]$-即使ℓ受常数限制也很难；我们为由ℓ，r和$\mathrm{\Delta }（G）$，并且我们证明问题的这种版本不接受多项式内核，除非 $\text{NP}\subseteq \text{coNP / poly}$。最后，我们在分割图和图形上分析S-TCP。