  We study techniques for solving the Maximum Satisfiability problem (MaxSAT).
Our focus is on variables of degree 4. We identify cases for degree-4 variables
and show how the resolution principle and the kernelization techniques can be
nicely integrated to achieve more efficient algorithms for the MaxSAT problem.
As a result, we present an algorithm of time $O^*(1.3248^k)$ for the MaxSAT
problem, improving the previous best upper bound $O^*(1.358^k)$ by Ivan
Bliznets and Alexander.
