A Note on the Seven Bridges of Königsberg Problem

• Autorzy: Adam Naumowicz
• Języki publikacji: EN

Abstrakty

EN

In this paper we account for the formalization of the seven bridges of Königsberg puzzle. The problem originally posed and solved by Euler in 1735 is historically notable for having laid the foundations of graph theory, cf. [7]. Our formalization utilizes a simple set-theoretical graph representation with four distinct sets for the graph’s vertices and another seven sets that represent the edges (bridges). The work appends the article by Nakamura and Rudnicki [10] by introducing the classic example of a graph that does not contain an Eulerian path. This theorem is item #54 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http://www.cs.ru.nl/F.Wiedijk/100/.

Słowa kluczowe

EN

Eulerian paths; Eulerian cycles; Königsberg bridges problem

Kategorie tematyczne

• 05C62: Graph representations (geometric and intersection representations, etc.) {For graph drawing, see also }
• 03B35: Mechanization of proofs and logical operations
• 05C45: Eulerian and Hamiltonian graphs

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2014
• Tom: 22
• Numer: 2
• Strony: 177-178

Daty

online

2015-02-05

Twórcy

autor

Adam Naumowicz

• Institute of Informatics University of Białystok Sosnowa 64, 15-887 Białystok Poland

Bibliografia

• [1] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91–96, 1990.
• [2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107–114, 1990.
• [3] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1): 55–65, 1990.
• [4] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153–164, 1990.
• [5] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47–53, 1990.
• [6] Czesław Byliński and Piotr Rudnicki. The correspondence between monotonic many sorted signatures and well-founded graphs. Part I. Formalized Mathematics, 5(4):577– 582, 1996.
• [7] Gary Chartrand. Introductory Graph Theory. New York: Dover, 1985.
• [8] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165–167, 1990.
• [9] Krzysztof Hryniewiecki. Graphs. Formalized Mathematics, 2(3):365–370, 1991.
• [10] Yatsuka Nakamura and Piotr Rudnicki. Euler circuits and paths. Formalized Mathematics, 6(3):417–425, 1997.
• [11] Andrzej Trybulec. Enumerated sets. Formalized Mathematics, 1(1):25–34, 1990.
• [12] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67–71, 1990.
• [13] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73–83, 1990. Received June 16, 2014

Identyfikatory

DOI

10.2478/forma-2014-0018