Abstract
The Four Color Conjecture is a well-known coloring problem of graphs. Since its advent, there are a lot of solvers. One of the early pioneers was Percy John Heawood, who has proved the Five Color Theorem. In addition, Kempe first demonstrated an important conclusion about planar graph: in any map, there must be a country with five or fewer neighbors. Kempe’s proof proposed two important concepts—“configuration” and “reducibility”, which laid the foundation for further solving the Four Color Problem. The Four Color Problem had previously been proved by use of computer. Based on Kempe’s concepts of “configuration” and “reducibility”, this paper attempts to provide a non-computer proof of the Four Color Problem through rigorous logical analysis.
Highlights
The Four Color Conjecture, known as the Four Color Problem, was first proposed by Francis Guthrie, an Englishman, in 1852 [1] [2] [3]
Kempe first demonstrated an important conclusion about planar graph: in any map, there must be a country with five or fewer neighbors
The Four Color Problem had previously been proved by use of computer
Summary
The Four Color Conjecture (hereinafter referred to as 4CC), known as the Four Color Problem, was first proposed by Francis Guthrie, an Englishman, in 1852 [1] [2] [3]. Its description is as follows: Give you a map of several countries. No neighboring countries can be colored the same color. Is it enough to use only four colors? One of the early pioneers was Percy John Heawood, who has proved the Five Color Theorem, that is, any map at most five colors is enough [4] [5]!. Between 1878 and 1880, Alfred Kempe and Peter Guthrie Tait, respectively, announced that they had proved 4CC. In 1890, Percy John Heawood pointed out Kempe’s holes in his proof.
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