Related papers: The choosability version of Brooks' theorem -- a s…

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.

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

We give a new proof of Brooks' theorem that immediately implies a strengthening of Brooks' theorem, known as Catlin's theorem.

Lov\'asz gave a short proof of Brooks' theorem by coloring greedily in a good order. We give a different short proof by reducing to the cubic case. Then we show how to extend the result to (online) list coloring via the Kernel Lemma.

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

We give a simple short proof of Brooks' theorem using only induction and greedy coloring, while avoiding issues of graph connectivity. The argument generalizes easily to some extensions of Brooks' theorem, including its variants for list…

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.

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.

In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.

A very short proof of Kneser's theorem via transversal is given.

We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.

Based on various strategies, we obtain several simple proofs of the celebrated Sharkovsky cycle coexistence theorem.

In this note, we present a simple directed graph proof of Sharkovsky's theorem.

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

We give a short and relatively elementary proof of the Hilton-Milner Theorem.

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.

In this paper we present a short and elementary proof for the error in Simpson's rule.

We give a counting based proof of the Graham Pollak Theorem

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