# A Note on the Seven Bridges of Königsberg Problem

Formalized Mathematics (2014)

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

## Access Full Article

top## Abstract

top## How to cite

topAdam 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

top- [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

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.