DNA solution based on triangle subgraph to the vertex cover problem

Abstract

DNA solution based on triangle subgraph to the vertex cover problem is given by means of an improved polynomial transformation from the vertex cover problem to the Hamiltonian circle problem. For an instance of the vertex cover problem, construct the triangle subgraph of each edge, which has 3 vertices and 3 edges instead of 4 vertices and 4 edges. And then link the triangle subgraphs of the edges incident to one vertex to form one sub path, and link the start and end points of each subpath to each selection vertex. Thus, the instance of the vertex cover problem is converted to that of the Hamiltonian circle problem, and DNA solution based on triangle subgraph to the vertex cover problem is given by means of the improved polynomial transformation.