Related papers: Four proofs of the directed Brooks' Theorem
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 give a new proof of Brooks' theorem that immediately implies a strengthening of Brooks' theorem, known as Catlin's theorem.
Arguably the simplest variation of this style of proof as we avoid reducing to the cubic case entirely.
A comprehensive review on Cook's contribution in the theory of NP-Completeness with relations to modern mathematics.
Recently we have obtained two simple proofs of Sharkovsky's theorem, one with directed graphs [7] and the other without [8]. In this note, we present yet more simple proofs of Sharkovsky's theorem.
An technically interesting proof of a known theorem.
We give a new proof of Lucas' Theorem in elementary number theory.
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…
We sketch several proofs of F\'ary--Milnor theorem.
We prove several extensions of the Erdos-Fuchs theorem.
This paper presents a short and simple proof of the Four-Color Theorem that can be utterly checkable by human mathematicians, without computer assistance. The new key idea that has allowed it and the global structure of the proof are…
Boolos's proof of incompleteness is extended straightforwardly to yield simple ``diagonalization-free'' proofs of some classical limitative theorems of logic.
We proved three theorems of $S$-version of the mulyiplicity one.
We prove that persuasion is an NP-complete problem.
In [3, Theorem 6.7B], the authors use the Main Theorems of Brauer to give a proof of Burnside's Normal $p$-complement Theorem. Unfortunately, the proof contains an error. We take this opportunity to give a proof along similar lines,…
In this note, we present a simple directed graph proof of Sharkovsky's theorem.
We prove that the quiver problem is NP complete.
In this paper, we provide an easy proof of the Four-colour Theorem in a special case indeed.
Here we give a short survey of our new results. References to the complete proofs can be found in the text of this article and in the litterature.