A Note on the Seven Bridges of Königsberg Problem

Adam Naumowicz

Formalized Mathematics (2014)

  • Volume: 22, Issue: 2, page 177-178
  • ISSN: 1426-2630

Abstract

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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/.

How to cite

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Adam Naumowicz. "A Note on the Seven Bridges of Königsberg Problem." Formalized Mathematics 22.2 (2014): 177-178. <http://eudml.org/doc/268696>.

@article{AdamNaumowicz2014,
abstract = {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/.},
author = {Adam Naumowicz},
journal = {Formalized Mathematics},
keywords = {Eulerian paths; Eulerian cycles; Königsberg bridges problem},
language = {eng},
number = {2},
pages = {177-178},
title = {A Note on the Seven Bridges of Königsberg Problem},
url = {http://eudml.org/doc/268696},
volume = {22},
year = {2014},
}

TY - JOUR
AU - Adam Naumowicz
TI - A Note on the Seven Bridges of Königsberg Problem
JO - Formalized Mathematics
PY - 2014
VL - 22
IS - 2
SP - 177
EP - 178
AB - 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/.
LA - eng
KW - Eulerian paths; Eulerian cycles; Königsberg bridges problem
UR - http://eudml.org/doc/268696
ER -

References

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  6. [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. [7] Gary Chartrand. Introductory Graph Theory. New York: Dover, 1985. 
  8. [8] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165–167, 1990. 
  9. [9] Krzysztof Hryniewiecki. Graphs. Formalized Mathematics, 2(3):365–370, 1991. 
  10. [10] Yatsuka Nakamura and Piotr Rudnicki. Euler circuits and paths. Formalized Mathematics, 6(3):417–425, 1997. 
  11. [11] Andrzej Trybulec. Enumerated sets. Formalized Mathematics, 1(1):25–34, 1990. 
  12. [12] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67–71, 1990. 
  13. [13] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73–83, 1990. Received June 16, 2014 

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