Related papers: Gallai's Theorem
In this paper, we give a detailed account of Goldfeld's proof of Siegel's theorem. Particularly, we present complete proofs of the nontrivial assumptions made in his paper.
In this paper we prove the WALA conjecture.
We derive the Gallai-Edmonds Structure Theorem from Hall's Theorem.
We give a counting based proof of the Graham Pollak Theorem
In this paper, we provide an easy proof of the Four-colour Theorem in a special case indeed.
The analogue of Goldie's Theorem for prime rings is proved for rings graded by abelian groups, eliminating unnecessary additional hypotheses used in earlier versions.
Torelli's theorem is proven by the study of the convolution product of the intersection cohomology sheaf of the thetadivisor.
We generalize a result of Tibor Gallai as follows: for any finite set of points $\mathcal{S}$ in the plane, if the plane is colored in finitely many colors, then there exist $2^{\aleph_0}$ monochromatic subsets of the plane homothetic to…
I present a simple, elementary proof of Morley's theorem, highlighting the naturalness of this theorem.
In this paper we go on to discuss about Stanley's theorem in Integer partitions. We give two different versions for the proof of the generalization of Stanley's theorem illustrating different techniques that may be applied to profitably…
This paper has been withdrawn by the author due to a crucial error in last part of proof.
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.
The result of this paper is proved in arXiv:1112.1163
The better title is "Yet another FALSE proof of the 4-colour theorem." Please consider all versions of this paper as historical material on the way to a non-computer proof of the 4-colour theorem. Interpreted as proofs, all versions are…
This is an exposition of Gauss's proof of Descartes's rule of signs.
A generalization of the law of total covariance is presented and proved.
A proof is given of Rosenthal's \(\ell_1\) theorem.
We note that an argument by Rogers (1958) gives a proof of Vaaler's theorem (1979) about sections of the cube and allows certain generalizations of the theorem.
The purpose of this paper is to present a generalization of Forelli's theorem. In particular, we prove an all dimensional version of the two-dimensional theorem of Chirka of 2005.
A Gallai coloring is an edge coloring that avoids triangles colored with three different colors. Given integers $e_1\ge e_2 \ge \dots \ge e_k$ with $\sum_{i=1}^ke_i={n \choose 2}$ for some $n$, does there exist a Gallai $k$-coloring of…