Related papers: A manual proof of the Four-colour Theorem
The paper contains an alternative proof of M. Kontsevich Formality Theorem.
We prove a local version of the Mazur-Ulam theorem.
We prove that compact topological 4-manifolds can be effectively presented by a finite amount of data.
In this work we state a Theorem on number theory and apply it to solve some ordinary and partial differential equations.
I give a proof of the uniform boundedness theorem that is elementary (i.e. does not use any version of the Baire category theorem) and also extremely simple.
We prove that every digraph has a vertex 4-colouring such that for each vertex $v$, at most half the out-neighbours of $v$ receive the same colour as $v$. We then obtain several results related to the conjecture obtained by replacing 4 by…
We prove several extensions of the Erdos-Fuchs theorem.
In this note we shall give a new proof to a quadrature formulae due to Newton.
In this note we give two proofs of Brooks' Theorem. The first is obtained by modifying an earlier proof and the second by combining two earlier proofs. We believe these proofs are easier to teach in Computer Science courses.
We prove that if one colors each point of the Euclidean plane with one of five colors, then there exist two points of the same color that are either distance $1$ or distance $2$ apart.
A $t$-tone coloring of a graph $G$ assigns to each vertex a set of $t$ colors such that any pair of vertices $u, v$ with distance $d$ can share at most $d-1$ colors. In this note, we prove several new results on $t$-tone coloring. For…
We prove that every finite colouring of the plane contains a monochromatic pair of points at an odd distance from each other.
In a recent paper, Dousse introduced a refinement of Siladi\'c's theorem on partitions, where parts occur in two primary and three secondary colors. Her proof used the method of weighted words and $q$-difference equations. The purpose of…
We give an infinite number of proofs of Pythagoras theorem.Some can be classified as `self-similar proofs'.
We give a full, correct proof of the following result, earlier claimed by Erd\H{o}s and Komj\'ath. If the Continuum Hypothesis holds then there is a coloring of the plane with countably many colors, with no monocolored right triangle.
Proofs of Tychonoff's theorem often seem to require a bit of magic. Machinery such as ultrafilters, nets or maximal families with the finite intersection property are employed to give proofs that can be very neat, but not the kind of thing…
This paper contains a detailed, self contained and more streamlined proof of our $l^2$ decoupling theorem for hypersurfaces.
In this paper we have given a unified graph coloring algorithm for planar graphs. The problems that have been considered in this context respectively, are vertex, edge, total and entire colorings of the planar graphs. The main tool in the…
The current status of the theory of and the experimental evidence for color transparency are reviewed. The problems with interpretation of quasielastic scattering on nuclei are discussed to some detail.
We provide elementary proof of several congruences involving single sum and multisums of binomial coefficients.