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In this paper, we use a new method to decrease the parameterized complexitybound for finding the minimum vertex cover of connected max-degree-3 undirectedgraphs. The key operation of this method is reduction of the size of aparticular subset of edges which we introduce in this paper and is called as"real-cycle" subset. Using "real-cycle" reductions alone we compute acomplexity 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 tobe $O(1.1504^k)$. This is currently the best complexity bound.

Improved Complexity Bound of Vertex Cover for Low degree Graph