Related papers: A mathematical proof of four color theorem
This paper has been withdrawn by the author due to an error in the last paragraph of step 2 of the main proof, on page 6.
The four-color conjecture has puzzled mathematicians for over 170 years and has yet to be proven by purely mathematical methods. This series of articles provides a purely mathematical proof of the four-color conjecture, consisting of two…
This paper has been withdrawn by the author, due a crucial error in the main idea.
This paper has been withdrawn by the author due to a crucial error in the submission action.
In this paper, we give a proof for four color theorem(four color conjecture). Our proof does not involve computer assistance and the most important is that it can be generalized to prove Hadwiger Conjecture. Moreover, we give algorithms to…
This paper has been withdrawn by the author.
This paper has been withdrawn by the author due to a crucial error in the proof of Theorem 1.
The paper has been withdrawn by the author, due to it being fundamentally flawed. The author apologizes for any inconvenience it may have caused.
This paper has been withdrawn by the author(s), due a crucial sign error in conclusion .
In [J. Combin. Theory Ser. B 70 (1997), 2-44] we gave a simplified proof of the Four-Color Theorem. The proof is computer-assisted in the sense that for two lemmas in the article we did not give proofs, and instead asserted that we have…
This paper has been withdrawn by the author due to a serious mistake on Lemma 2.4.
For the four-color theorem that has been developed over one and half centuries, all people believe it right but without complete proof convincing all1-3. Former proofs are to find the basic four-colorable patterns on a planar graph to…
This paper has been withdrawn by the author due to a crucial error.
This paper has been withdrawn by the author due to an erro thereon line -2 of page 4.
This paper has been withdrawn by the author due to a mistake in the proof of the main theorem.
This paper has been withdrawn by the authors due to an error.
This paper has been withdrawn by the author due to extremely unscientific errors.
This paper has been withdrawn by the author due to a crucial mistakes.
This paper has been withdrawn by the author, due a crucial mistake in proof of lemma 4.2.
This paper has been withdrawn by the author due to a crucial sign error in equation 1.