The following sketch of a city plan depicts 7 bridges: (a) Show that one cannot start walking from some place, cross each of the bridges exactly once, and come back to the starting place (no swimming please). Can one cross each bridge exactly once if it is not required to return to the starting position? This is a historical motivation for the notion of the Eulerian graphs. The scheme (loosely) corresponds to a part of the city of Königsberg, Královec, Królewiec, or Kaliningrad that's what it was variously called during its colorful history and the problem was solved by Euler in 1736. Can you find the city on a modern map? (b) How many bridges need to be added (and where) so that a closed tour exists?
The following sketch of a city plan depicts 7 bridges: (a) Show that one cannot start walking from some place, cross each of the bridges exactly once, and come back to the starting place (no swimming please). Can one cross each bridge exactly once if it is not required to return to the starting position? This is a historical motivation for the notion of the Eulerian graphs. The scheme (loosely) corresponds to a part of the city of Königsberg, Královec, Królewiec, or Kaliningrad that's what it was variously called during its colorful history and the problem was solved by Euler in 1736. Can you find the city on a modern map? (b) How many bridges need to be added (and where) so that a closed tour exists?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The following sketch of a city plan depicts 7 bridges:
(a) Show that one cannot start walking from some place, cross each
of the bridges exactly once, and come back to the starting place (no
swimming please). Can one cross each bridge exactly once if it is not
required to return to the starting position?
This is a historical motivation for the notion of the Eulerian graphs.
The scheme (loosely) corresponds to a part of the city of Königsberg,
Královec, Królewiec, or Kaliningrad that's what it was variously
called during its colorful history and the problem was solved by Euler
in 1736. Can you find the city on a modern map?
(b) How many bridges need to be added (and where) so that a closed
tour exists?
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