The seminal book on graph theory by Dénes Kőnig, published in the year 1936, collected notions and results from precursory works from the mid to late nineteenth century by Hamilton, Cayley, Sylvester and others. More importantly, Kőnig himself contributed many of his own results that he had obtained in the more than twenty years that he had been working on this subject matter. What is noteworthy is the fact that the fundamentals of what he calls directed graphs are taken almost exhaustively from Paul Hertz' 1922 article on structural reasoning about sentences of the form . This is not a fact that is well known in logical circles, even though Kőnig fully acknowledges this in his book. In view of the numerous trends in the recent decades to describe and explicate logical matters by means of graphs, the fact that it was Hertz' foundation of structural reasoning that informed basic notions of graph theory in the first place is highly significant. The main goal of this paper is to summarize Hertz' article and demonstrate how Kőnig integrates the notions and results presented therein in his book. This is followed by an exposition of how and when Hertz' results were reinvented in terms of graph theory. A critical discussion of the opinion expressed by both Hertz and Kőnig that the more general sentences of the form , introduced by Hertz in a companion article in 1923, cannot be interpreted by graphs concludes this paper.

中文翻译：

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结构推理在图论起源中的作用

Dénes Kőnig 于 1936 年出版的关于图论的开创性著作收集了 Hamilton、Cayley、Sylvester 等人从 19 世纪中后期的先驱著作中收集的概念和结果。更重要的是，Kőnig 本人贡献了他在这个主题上工作 20 多年所获得的许多自己的成果。值得注意的是，他所谓的有向图的基本原理几乎完全取自 Paul Hertz 1922 年关于形式句子结构推理的文章。尽管 Kőnig 在他的书中完全承认了这一点，但这在逻辑界并不是众所周知的事实。鉴于近几十年来通过图表来描述和解释逻辑问题的众多趋势，事实是赫兹的 结构推理的基础，首先告知图论的基本概念是非常重要的。本文的主要目标是总结 Hertz 的文章，并展示 Kőnig 如何整合他书中提出的概念和结果。接下来是关于赫兹的结果如何以及何时在图论方面被重新发明的说明。对 Hertz 和 Kőnig 表达的观点的批判性讨论，即 Hertz 在 1923 年的一篇同伴文章中引入的更一般的形式的句子不能用图表来解释，本文得出结论。文章并演示 Kőnig 如何整合他书中提出的概念和结果。接下来是关于赫兹的结果如何以及何时在图论方面被重新发明的说明。对 Hertz 和 Kőnig 表达的观点的批判性讨论，即 Hertz 在 1923 年的一篇配套文章中引入的更一般的形式的句子不能用图表来解释，本文得出结论。文章并演示 Kőnig 如何整合他书中提出的概念和结果。接下来是关于赫兹的结果如何以及何时在图论方面被重新发明的说明。对 Hertz 和 Kőnig 表达的观点的批判性讨论，即 Hertz 在 1923 年的一篇配套文章中引入的更一般的形式的句子不能用图表来解释，本文得出结论。