The maximum independent set problem is a basic NP-hard problem and has
been extensively studied in exact algorithms. The maximum independent
set problems in low-degree graphs are also important and may be
bottlenecks of the problem in general graphs. In this paper, we present
an $O^*(1.1737^n)$-time exact algorithm for the maximum independent set
problem in an $n$-vertex graph with degree bounded by $5$, improving the
previous running time bound of $O^*(1.1895^n)$. In our algorithm, we
introduce an effective divide-and-conquer procedure to deal with vertex
cuts of size at most two in graphs, and design branching rules on some
special structure of triconnected graphs of maximum degree 5. These
result in an improved algorithm without introducing a large number of
branching rules.