Graphs and matrices: A translation of "Graphok \'{e}s matrixok" by D\'{e}nes K\H{o}nig (1931)

TL;DR

This paper explores K"onig's theorem, establishing the equivalence of minimum vertex cover and maximum matching in bipartite graphs, and discusses the relationship between graphs and matrices with combinatorial insights.

Contribution

It provides a translation and analysis of K"onig's original 1931 work, highlighting the connection between bipartite graph properties and matrix representations.

Findings

Proves K"onig's theorem for bipartite graphs

Discusses the relationship between graphs and matrices

Provides combinatorial observations on matrix properties

Abstract

This paper, originally written in Hungarian by D\'{e}nes K\H{o}nig in 1931, proves that in a bipartite graph, the minimum vertex cover and the maximum matching have the same size. This statement is now known as K\H{o}nig's theorem. The paper also discusses the connection of graphs and matrices, then makes some observations about the combinatorial properties of the latter.