Related papers: Four proofs of the directed Brooks' Theorem

We make an attempt at proving the Four Colour Theorem in six pages.

We prove two theorems on cohomologically complete complexes. These theorems are inspired by, and yield an alternative proof of, a recent theorem of P. Schenzel on complete modules.

We give a new simpler proof of a theorem of Jayne and Rogers.

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.

We give a proof of the Marker-Steinhorn Theorem which fills a gap in previous proofs of the result.

Our goal in the present paper is to give a new ergodic proof of a well-known Veech's result, build upon our previous works.

In this paper we present a more transparent upgrade of our proofs and comment on Jerabek's paper [8].

A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.

We present a simpler way than usual to deduce the completeness theorem for the second-oder classical logic from the first-order one. We also extend our method to the case of second-order intuitionistic logic.

We provide a complete proof of an optimal version of the Marcinkiewicz multiplier theorem.

This is the second of three papers about the Compression Theorem. We give proofs of Gromov's theorem on directed embeddings [M Gromov, Partial differential relations, Springer--Verlag (1986); 2.4.5 C'] and of the Normal Deformation Theorem…

We prove three variations of recent results due to Andrews on congruences for $NT(m,k,n)$, the total number of parts in the partitions of $n$ with rank congruent to $m$ modulo $k$. We also conjecture new congruences and relations for…

In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…

Simple and shorter proofs of two Dirac-type theorems involving connectivity are presented.

We give a new proof of the theorem of Kronecker-Weber based on Kummer theory and Stickelberger's theorem.

We prove a new q-analogue of Nicomachus's Theorem about the sum of cubes and some related results.

We announce numerous new results in the theory of orthogonal polynomials on the unit circle.

This short note present a "proof" of $P\neq NP$. The "proof" with double quotation marks is to indicate that we do not know whether the proof is correct or not (We're confused because we do know in which we make the mistakes).

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

A new viewpoint of the G\"odel's incompleteness theorem be given in this article which reveals the deep relationship between the logic and computation. Upon the results of these studies, an algorithm be given which shows how to search a…