Related papers: A mathematical proof of four color theorem
This paper has been withdrawn by the author due to a crucial error in equation (51).
A formal proof has not been found for the four color theorem since 1852 when Francis Guthrie first conjectured the four color theorem. Why? A bad idea, we think, directed people to a rough road. Using a similar method to that for the formal…
A simpler proof of the four color theorem is presented. The proof was reached using a series of equivalent theorems. First the maximum number of edges of a planar graph is obatined as well as the minimum number of edges for a complete…
This paper has been withdrawn by the author due to a crucial sign error in Theorem 3.4.
This paper has been withdrawn by author due to an error in the proof.
This paper has been withdrawn by the author due to a crucial sign error in equation 1.
This paper has been withdrawn by the authors due to some fatal errors in the analysis.
This paper has been withdrawn by the author due to a crucial errors.
This paper has been withdrawn by the authors due to crucial error in the main proof (located in Section 2.4). The authors apologize for any inconveniences.
The four-color theorem states that no more than four colors are required to color all nodes in planar graphs such that no two adjacent nodes are of the same color. The theorem was first propounded by Francis Guthrie in 1852. Since then,…
This paper has been withdrawn by the author due to a crucial error in Lemma 3.5.
This paper has been withdrawn by the author due to the presented idea is wrong.
This paper has been withdrawn by the author due to an error.
This paper has been withdrawn by the author, due to a significant error in section 4.3.1.
Four-Color Theorem has secret in its logical proof and actual operating. In this paper we will give a proof of Four-Color Theorem based on Kuratowski's Theorem using some induction argument and give a description of the most complicated…
This paper has been withdrawn by the author due to a critical error in the proof of Theorem A pointed out by Burkhard Wilking.
This paper has been withdrawn by the author due to an error in the main proof (thanks to Carlos D'Andrea)
This paper has been withdrawn by the author due to the unsure solutions to the Dyson-Schwinger equation.
This paper has been withdrawn by the author due to a gap in the proof of the main result.
This paper has been withdrawn by the author due to an error in the derivation.