Related papers: Yet another short proof of the 4-colour theorem

This paper has been withdrawn by the author.

The status of the theory of color confinemnt is discussed.

This paper has been withdrawn by the author. Peterson and Woodall previously proved that the list-edge-colouring conjecture holds for graphs without odd cycles of length 5 or longer. D. Peterson and D. R. Woodall, Edge-choosability in…

The purpose of this erratum is to correct a mistake in the proof of Theorem 4.1 of our paper \cite{CF}.

A triangulation of a polygon is a subdivision of it into triangles, using diagonals between its vertices. Two different triangulations of a polygon can be related by a sequence of flips: a flip replaces a diagonal by the unique other…

This paper has been withdrawn by the author(s), due an error in the proof.

The Cyclic Coloring Conjecture asserts that the vertices of every plane graph with maximum face size D can be colored using at most 3D/2 colors in such a way that no face is incident with two vertices of the same color. The Cyclic Coloring…

We present a new proof of the known fact that the chromatic number of the plane is at least 5. The main difference of this proof is that it can be verified manually without the help of the computer.

In this short paper we review and extract some features of the Fredholm Alternative problem .

We give an infinite number of proofs of Pythagoras theorem.Some can be classified as `self-similar proofs'.

In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.

The Four color problem is closely related to other branches of mathematics and practical applications. More than 20 of its reformulations are known, which connect this problem with problems of algebra, statistical mechanics and planning.…

We prove several extensions of the Erdos-Fuchs theorem.

We will give a simple proof of the ambiguous class number formula.

In this paper, an algorithm for determining 3-colorability, i.e. the decision problem (YES/NO), in planar graphs is presented. The algorithm, although not exact (it could produce false positives) has two very important features: (i) it has…

This paper considers the problem of showing that every pair of binary trees with the same number of leaves parses a common word under a certain simple grammar. We enumerate the common parse words for several infinite families of tree pairs…

This paper has been withdrawn by the author(s), due an error in the proof.

In this article, we give two different proofs of why the Collatz Conjecture is false.

The story on the early days of the Quantum Ergodic Theorem. Alternative proof, underlying heuristics, physical analogies and interpretations.

We give a new proof of Lucas' Theorem in elementary number theory.