Related papers: A mathematical proof of four color theorem

This paper has been withdrawn by the author(s), due a crucial sign error in Thm. 11.

This paper has been withdrawn by the author, due to a crucial error in the proof of Thm.1

This paper has been withdrawn by the author due to a crucial error.

This paper has been withdrawn by the author(s), due an error in the proof.

This paper has been withdrawn by the author, due an error in claim 1.

This paper has been withdrawn by the author due to a crucial argument error at p.10.

This paper has been withdrawn due to an error in the proof of the main theorem.

This paper has been withdrawn by the author because there are some typos in proofs.

This paper has been withdrawn by the author due to a crucial sign error in equation 1.

This paper has been withdrawn by the author [arXiv admin].

This paper has been withdrawn by the author due to a errors in figure 3,4

In this paper we have investigated some old issues concerning four color map problem. We have given a general method for constructing counter-examples to Kempe's proof of the four color theorem and then show that all counterexamples can be…

This paper has been withdrawn by the author as it has already been submitted under the title "Twisted character of a small Representation of GL(4)".

This paper has been withdrawn because of serious errors.

This paper has been withdrawn due to a critical error discovered in Theorem 4.21. Anyone with a historical or pragamatic interest in prior "negative results", however - e.g., failed proof attempts relating to the (in)consistency of ZF or…

This paper has been withdrawn by the author for further investigation.

This paper has been withdrawn by the author.

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This paper has been withdrawn by the authors due to a gap in the proof of the main result (in 5.3).

This paper has been withdrawn by the author due to an error.