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

We show that some mathematical results and their negations are both deducible. The derived contradictions indicate the inconsistency of current mathematics. This paper is an updated version of arXiv:math/0606635v3 with additional results…

We answer the question in the title in the negative by providing four proofs.

The main result of this paper is a "colored Tverberg theorem for rainbow-unavoidable complexes". This theorem may be considered as a merging of two theorems: "Tverberg theorem for collectively unavoidable complexes" and "balanced colored…

In this article using elementary school level Geometry we observe an alternative proof of Pythagorean Theorem from Heron's Formula.

A very short proof of Kneser's theorem via transversal is given.

In this paper we present a proof of the BMZ Reduction Lemma with a motivational perspective, and state this lemma for maps to manifolds using the classical definition of cohomological dimension. The lemma, proved and utilized in [4], gives…

Gallai's colouring theorem states that if the edges of a complete graph are 3-coloured, with each colour class forming a connected (spanning) subgraph, then there is a triangle that has all 3 colours. What happens for more colours: if we…

The paper presents a counterexample to the Hodge conjecture.

We present the proof of the equivalence theorem in quantum field theory which is based on a formulation of this problem in the field-antifield formalism. As an example, we consider a model in which a different choices of natural finite…

Recently the ``Fluctuation theorem'' has been criticized and incorrect incorrect contents have been atributed to it. Here I reestablish and comment the original statements.

Coloring planar Feynman diagrams in spinor quantum electrodynamics, is a non trivial model soluble without computer. Four colors are necessary and sufficient.

We give a proof of Brooks' theorem and its list coloring extension using the algebraic method of Alon and Tarsi; this also shows that the Brooks' theorem remains valid in a more general game coloring setting.

In this paper, we give a simple counter example to the famous Hodge conjecture.

This paper has been withdrawn since it is identical to the paper math.QA/0601267. It was posted by mistake.

We correct a partial mistake for a metric presented in the article "Lattice constellation and codes from quadratic number fields" [IEEE Trans. Inform. Theory, vol. 47, No. 4, May. 2001]. We show that the metric defined in the article is not…

Comment on Classifier Technology and the Illusion of Progress [math.ST/0606441]

Comment on Classifier Technology and the Illusion of Progress [math.ST/0606441]

The aim of this paper is to prove a version of Lie's theorem for the supertropical algebra.

This material is dedicated to the estimation of the chromatic number and chromatic class of the conjugated triangulation (first conversion) and also of the second conversion of the planar triangulation. Also this paper introduces some new…

Let $H$ be a 2-regular graph and let $G$ be obtained from $H$ by gluing in vertex-disjoint copies of $K_4$. The "cycles plus $K_4$'s" problem is to show that $G$ is 4-colourable; this is a special case of the \emph{Strong Colouring…