  The Subset Feedback Vertex Set problem (SFVS), to delete $k$ vertices from a
given graph such that any vertex in a vertex subset (called a terminal set) is
not in a cycle in the remaining graph, generalizes the famous Feedback Vertex
Set problem and Multiway Cut problem. SFVS remains NP-hard even in split and
chordal graphs, and SFVS in Chordal Graphs (SFVS-C) can be considered as an
implicit 3-Hitting Set problem. However, it is not easy to solve SFVS-C faster
than 3-Hitting Set. In 2019, Philip, Rajan, Saurabh, and Tale (Algorithmica
2019) proved that SFVS-C can be solved in $\mathcal{O}^{*}(2^{k})$ time,
slightly improving the best result $\mathcal{O}^{*}(2.076^{k})$ for 3-Hitting
Set. In this paper, we break the "$2^{k}$-barrier" for SFVS-C by giving an
$\mathcal{O}^{*}(1.820^{k})$-time algorithm. Our algorithm uses reduction and
branching rules based on the Dulmage-Mendelsohn decomposition and a
divide-and-conquer method.
