相关论文: A unified proof of Brooks' theorem and Catlin's th…

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 present a short and self-contained proof of the choosability version of Brooks' theorem.

We prove a generalization of Lopes's theorem, that is, of the converse of Brolin's theorem.

We give four new proofs of the directed version of Brook's Theorem and an NP-completeness result.

We give a new proof of Lucas' Theorem in elementary number theory.

Arguably the simplest variation of this style of proof as we avoid reducing to the cubic case entirely.

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 new simpler proof of a theorem of Jayne and Rogers.

In this note we show that any proof of Wallis's formula or of the probability integral formula proves both assertions.

New version, including a variant of Quillen's proof of the Solomon-Tits theorem.

An technically interesting proof of a known theorem.

A proof is given of Rosenthal's \(\ell_1\) theorem.

This article describes a new proof of the equality condition for the Brunn-Minkowski inequality.

We give a short proof of a strengthening of the Maximal Ergodic Theorem which also immediately yields the Pointwise Ergodic Theorem.

In this paper, we give a refinement of a theorem by Franks, which answers two questions raised by Kang.

The paper gives a unified and simple proof of both theorems and Cousin's theorem.

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

The assumptions needed to prove Cox's Theorem are discussed and examined. Various sets of assumptions under which a Cox-style theorem can be proved are provided, although all are rather strong and, arguably, not natural.

We present a new proof of the celebrated quadratic reciprocity law. Our proof is based on group theory.

We give a counting based proof of the Graham Pollak Theorem