The Contradiction Argument for the Brouwer Conjecture

Abstract

Resumo. In this work we develop results to contribute to the study of the Brouwer conjecture through an argument of contradiction. Specifically, if the Brouwer conjecture is not valid for a graph and this graph respects some conditions, we show that the conjecture is also not valid for the graphs obtained by deleting an edge or vertex. In this way, we can recursively delete certain vertices and edges of the original graph until the resulting graph is in a family for which the conjecture is proven, a contradiction.