Related papers: A mathematical proof of four color theorem

This paper has been withdrawn by the author due to incomplete interpretation for the results.

This paper has been withdrawn by the authors due to an error in the main theorem.

The paper has been withdrawn due to a crucial error in section 3.

This paper has been withdrawn by the authors, due to a flaw in the proof of Theorem 1. This preprint is superseded by quant-ph/0610027, where a correct proof can be found. Thanks to Rainer Siegmund-Schultze for spotting the error.

This paper has been withdrawn.

This paper has been withdrawn by the author because eq.(4) and those subsequent are incorrect.

This paper has been withdrawn by the authors due to a fatal flaw in the central proof.

This submission has been withdrawn at the request of the author.

This paper has been withdrawn by the author due to the version of [A complete proof of Hamilton's conjecture] at arXiv:1008.1576

This paper has been withdrawn by the author due to an error in the proof of Proposition 4.8.

This paper has been withdrawn by the authors due to numerical problems to get viable results.

this paper has been withdrawn by the author due to crucial type errors

This paper has been withdrawn by the author because Lemma 3 is incorrect. This mistake is crucial in this paper.

This paper has been withdrawn by the author due to serious error found in main argument.

This paper has been withdrawn by the authors due to a crucial error.

This paper was withdrawn by the authors.

This paper has been withdrawn by the author due to the presented idea is wrong.

This paper has been withdrawn by the authors, due to a crucial error in beta functions.

This paper has been withdrawn by the author, due a crucial error in the optimization. For the last one month I have been trying to remove the error, but it seems to take a lot of time so I decided to withdraw this paper for the moment.

This paper has been withdrawn by the author due to a crucial error in the proof of Lemma 2.2.