Related papers: Gallai's Theorem

We prove a better coloring theorem for aleph_4 and even aleph_3. This has a general topology consequence.

In this article, I discuss material which is related to the recent proof of Fermat's Last Theorem: elliptic curves, modular forms, Galois representations and their deformations, Frey's construction, and the conjectures of Serre and of…

We prove a generalization of Tur\'{a}n's theorem proposed by Balogh and Lidick\'{y}.

In this paper we prove a generalization of famous Larchr's theorem concerning good lattice points.

We give a brief historical overview of the famous Pythagoras' theorem and Pythagoras. We present a simple proof of the result and dicsuss some extensions. We follow \cite{thales}, \cite{wiki} and \cite{wiki2} for the historical comments and…

In this note, the correction to the proof of one theorem in some our previous paper [arXiv:1302.0589] will be given.

Helly's theorem is a classical result concerning the intersection patterns of convex sets in $\mathbb{R}^d$. Two important generalizations are the colorful version and the fractional version. Recently, B\'{a}r\'{a}ny et al. combined the…

We give a pen and paper and (comparatively) much simpler proof to verify of the Four Colour Theorem.

In this paper, we give a proof for four color theorem(four color conjecture). Our proof does not involve computer assistance and the most important is that it can be generalized to prove Hadwiger Conjecture. Moreover, we give algorithms to…

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

In this paper, we give a more physical proof of Liouville's theorem for a class generalized harmonic functions by the method of parabolic equation.

A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.

This is a revised version of the preprint which has been available electronically for a while. The paper will now appear in J. Ramanujan Math. Soc.

In this note we give a detailed proof of a theorem of Aubin.

We propose in this paper a Galois theory of $q$-difference equations where q is a root of unity. This theory is the q difference analogue of the Galois theory of iterative differential equations, that is differential equations over fields…

Our point of departure is the following simple common generalisation of the Sylvester-Gallai theorem and the Motzkin-Rabin theorem: Let S be a finite set of points in the plane, with each point coloured red or blue or with both colours.…

For Fatou's interpolation theorem of 1906 we suggest a new elementary proof.

An edge colouring of $K_n$ with $k$ colours is a Gallai $k$-colouring if it does not contain any rainbow triangle. Gy\'arf\'as, P\'alv\"olgyi, Patk\'os and Wales proved that there exists a number $g(k)$ such that $n\geq g(k)$ if and only if…

This report presents a formalization of May's theorem in the proof assistant Coq. It describes how the theorem statement is first translated into Coq definitions, and how it is subsequently proved. Various aspects of the proof and related…

We prove modularity lifting theorems for l-adic Galois representations of any dimension satisfying a unitary type condition and a Fontaine-Laffaille type condition at l. This extends the results of Clozel, Harris and Taylor, and the…