  In this paper, we use a new method to decrease the parameterized complexity
bound for finding the minimum vertex cover of connected max-degree-3 undirected
graphs. The key operation of this method is reduction of the size of a
particular subset of edges which we introduce in this paper and is called as
"real-cycle" subset. Using "real-cycle" reductions alone we compute a
complexity bound $O(1.15855^k)$ where $k$ is size of the optimal vertex cover.
Combined with other techniques, the complexity bound can be further improved to
be $O(1.1504^k)$. This is currently the best complexity bound.
