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First edition. Graph Theory, 1736–1936 is a book in the history of mathematics on graph theory.It focuses on the foundational documents of the field, beginning with the 1736 paper of Leonhard Euler on the Seven Bridges of Königsberg and ending with the first textbook on the subject, published in 1936 by Dénes Kőnig.
Download as PDF; Printable version; ... Pages in category "Theorems in graph theory" ... (graph theory) Kotzig's theorem; Kuratowski's theorem; M.
De Bruijn–Erdős theorem (graph theory) De Finetti's theorem (probability) De Franchis theorem (Riemann surfaces) De Gua's theorem ; De Moivre's theorem (complex analysis) De Rham's theorem (differential topology) Deduction theorem ; Denjoy theorem (dynamical systems) Denjoy–Carleman theorem (functional analysis)
The first textbook on graph theory was written by Dénes Kőnig, and published in 1936. [26] Another book by Frank Harary , published in 1969, was "considered the world over to be the definitive textbook on the subject", [ 27 ] and enabled mathematicians, chemists, electrical engineers and social scientists to talk to each other.
The satisfiability problem for a sentence of monadic second-order logic is the problem of determining whether there exists at least one graph (possibly within a restricted family of graphs) for which the sentence is true. For arbitrary graph families, and arbitrary sentences, this problem is undecidable.
The De Bruijn–Erdős theorem for countable graphs can also be shown to be equivalent in axiomatic power, within a certain theory of second-order arithmetic, to Weak Kőnig's lemma. [ 16 ] For a counterexample to the theorem in models of set theory without choice, let G {\displaystyle G} be an infinite graph in which the vertices represent all ...
In graph theory, the handshaking lemma is the statement that, in every finite undirected graph, the number of vertices that touch an odd number of edges is even. For example, if there is a party of people who shake hands, the number of people who shake an odd number of other people's hands is even. [ 1 ]
In graph theory, Turán's theorem bounds the number of edges that can be included in an undirected graph that does not have a complete subgraph of a given size. It is one of the central results of extremal graph theory, an area studying the largest or smallest graphs with given properties, and is a special case of the forbidden subgraph problem on the maximum number of edges in a graph that ...