Great Floor Plan A Little Coloring Of Computer-aided Research

In the article we describe the conditions of a series of graphs'4-coloring. Basing on two programs (program getSome4colors and program getTfc) of professor Xu Shou-chun, we put forward the way of reinforcing search so as to increase the quantity of 4-coloring, and it makes program getTfc find out much more, indiscoverable and less points trees of 4-coloring so as to approach total number of 4-coloring of the graph. However, for a mass of graphs, "program getTfc" cannot find out all the 4-coloring results. So the way of reinforcing search is the supplement of it. We will get more 4-coloring results.In 1999, Professor XU Shou-chun found a way to solve the automorphism group~[1] of maximal planar graph with 4-coloring results. But the way requires to find out all 4-coloring results of the graph, to select a kind of 4-coloring results from them (For example, all path-path colorings), and to find out automorphism group of the graph finally. The algorithm of finding all 4-coloring results is exponential, it take about half past four hours to find out all the 4-coloring results for the graph g37a, so for the graphs of more than 100 points the computer will be of no effect. In the article, the 4-coloring results gotten through the above way will be classified, and a kind of path-path 4-coloring will be selected from them.At the moment we find that they can be classified three kinds, that is,pp1-type, pp2-type and pp3-type. Thereinto, it is easy to find out pp1-type 4-coloring with the computer. So we get a way that find out ppl-type directly, that is, "draw-out points way". It is the polynomial way that is successful to find out 4-coloring of more than 100s'graph. Take g102 for example, we introduce it.In the article we introduce the inducing four regular graph of maximal planar graph, and provide two structures of inducing four regular graph of maximal planar graph, their equivalence and their properties. Then we prove the one-to-one corresponding relation between 3-coloring of inducing four regular graph and 4-coloring of maximal planar graph and find out the relation between three colors of inducing four regular graph and three dual bi-chromatic subgraph of maximal planar graph. With the one-to-one corresponding relation we compile theprogram that find out ppl-type 4-coloring, that is, "draw-out edge way".