The 4-Color Theorem is Proved by Hand

EasyChair Preprint no. 5773

Abstract

We prove the four color theorem (briefly 4CT)by a new way, which is absolutely different from ones by A.B. Kempe in 1879 and P. Tait in 1880 as well as the computer-aided proofs by K. Appel and W. Haken in 1976 and by N. Robertson etc. in 1995.With a tier graph of the tier number being the least and two definitions: one is a vertex adjacent closed subgraph corresponding to v_i , another is the good independent sets; three conditions to get the first good independent set r₁ from any planar graph G had been found, by which V(G) can be partitioned into 4 independent sets.

Finally, we show in detail the entire procedure to prove the 4CT by a example.

Keyphrases: good independent set, Hub, Keywords—outer planar graph, tier graph, vertex adjacent closed subgraph

@Booklet{EasyChair:5773,
  author = {Xiurang Qiao},
  title = {The 4-Color Theorem is Proved by Hand},
  howpublished = {EasyChair Preprint no. 5773},

  year = {EasyChair, 2021}}