Study on Art Gallery Based on 4-coloring

It isn´t the best result on the art gallery based on the 3-coloring in resolving the most of simple polygons, through a analysis of the simple polygon triangulation in the relationship between adjacent triangles, using the dual relation between triangulation and binary tree, this paper puts a forward 4-coloring on the polygon triangulation, and analyze and research the case which has been 4-coloring. we can obtain some results that the condition of any type of colors could cover the whole polygon, and the condition that at least one type of colors could cover the whole polygon (namely the art gallery only need for monitors), we also analyzing the reason which failed to cover the whole polygon, and presenting the condition which couldn´t be 4-colored.