| At first, as professor Xu Shou Chun's theory (got the auto-isomorphic of maximal planar graph and judged isomorphic of maximal planar graph need the easiest type of 4-coloring) needed, this paper gave all types of 4-coloring a name and gave the sequence of how easy they are. So we can distinguish all kinds of 4-coloring,and got some 4-coloring type such as type-PP, type-PT, type-TT, type-SPP, type-SPT, type-STT, type-CPP, type-CPT, type-CTT...second, author battlemented ,perfected ,expanded professor Xu's project and program, got a new project of solving all 4coloring result of maximal planar graph's ,and performed it at program. Currently, it can solve all maximal planar graphs' 4coloring result at the scale of 40. There into it had solved a maximal planar graphs' all 4-coloring result which's order is 43. Using the new project, it had processed about 100 example maximal planar graphs at different degree and gave the records. As following, author gavethe statistic of all founded 4-coloring result, founded the statistic truth: from the type-PP to type-CPP it can overcast all gave example maximal planar graphs, and type-CPP (one type of simplest-no-tree-4-colring) overcast the most, simplest-no-tree-4-colring overcast the almost all gave example maximal planar graphs (except two examples g9d and g11h).Next, author found simplest-no-tree-4-colring has good proportion to 85.25% in all found 4-coloring result.Andg ave some characters of simplest-no-tree-4-colring's portion. Author proceed a batch of no-Hamilton graphs too, and got some acquaintanceship about no-Hamilton graphs, gave the concept ofbi(mi)-good-even-Hamilton-cycle, modified the guess of Tait. Author gave examples of maximal planar graph self-isomorphic and isomorphic using simplest-no-tree-4-colring 4-colring results.In the past half of this paper, Author gave three experiment projects to find simplest-no-tree-4-colring directly. At the point view of simplest-no-tree-4-colring' two connected tree partite, using the relationship of maximal planar graphs and its dual graphs, author then gave a project ----expand tree by graph's face. It can find all simplest-no-tree-4-colring under control. But it wastes too much time, so it can only suit 21 points graphs at most. In all had found 4-coloring results there are many results have not only one connected partite having cycles. If we transform a few of points' color we can got some new4-coloring results possibly. In these new 4-coloring results it maybe has simplest-no-tree-4-colring. Then it is the second project---the way of destroy cycle. But it must need some had found 4-coloring results. Project three are base on the truth that all 4-coloring algorithm's compute scale is increased by scale of exponent with the graph's order. So decreasing the order of graph is very important. Author base on the truth that many small tree appears frequently gave a project to decrease order. In gave examples, the order of graph is 59.Just from its twice decreased graph it also can got 1486 simplest-no-tree-4-colring results. But project three wastes much time too, and it loses some results unavoidable.At last author analyzed all had four coloring algorithm and found that we can't got a good algorithm to find simplest-no-tree-4-colring results. But we can expand the area of can proceed by using compositive projects that all mentioned above. And all of it can use for reference. |
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