\input zb-basic \input zb-ioport \iteman{io-port 05649473} \itemau{Paulusma, Dani\"el; van Rooij, Johan M.M.} \itemti{On partitioning a graph into two connected subgraphs.} \itemso{Dong, Yingfei (ed.) et al., Algorithms and computation. 20th international symposium, ISAAC 2009, Honolulu, Hawaii, USA, December 16--18, 2009. Proceedings. Berlin: Springer (ISBN 978-3-642-10630-9/pbk). Lecture Notes in Computer Science 5878, 1215-1224 (2009).} \itemab Summary: Suppose a graph $G$ is given with two vertex-disjoint sets of vertices $Z _{1}$ and $Z _{2}$. Can we partition the remaining vertices of $G$ such that we obtain two connected vertex-disjoint subgraphs of $G$ that contain $Z _{1}$ and $Z _{2}$, respectively? This problem is known as the 2-Disjoint Connected Subgraphs problem. It is already NP-complete for the class of $n$-vertex graphs $G = (V,E)$ in which $Z _{1}$ and $Z _{2}$ each contain a connected set that dominates all vertices in $V\backslash (Z _{1} \cup Z _{2})$. We present an ${\mathcal O}^*(1.2051^n)$ time algorithm that solves it for this graph class. As a consequence, we can also solve this problem in ${\mathcal O}^*(1.2051^n)$ time for the classes of $n$-vertex $P _{6}$-free graphs and split graphs. This is an improvement upon a recent ${\mathcal O}^*(1.5790^n)$ time algorithm for these two classes. Our approach translates the problem to a generalized version of hypergraph 2-coloring and combines inclusion/exclusion with measure and conquer. \itemrv{~} \itemcc{} \itemut{} \itemli{doi:10.1007/978-3-642-10631-6\_122} \end