2/10/14
CS109: Eulerian Circuits
www.cs.bu.edu/~best/courses/cs109/modules/euleriancircuits/
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Discussion on Eulerian Circuits
Goals:
Reinforce the point that graphs are useful modeling tools
Review graph terminologies
Go through proofs by contradiction and by induction
Plan:
1.
Start with the historical context of
Seven Bridges of Konigsberg
.
The story goes like this: There were seven bridges crossing the river Pregel in
the town of Konigsberg (18th century Prussia). See map and picture below.
Two of the remaining bridges of Konisgsberg (now
Kaliningrad in Russia
).
Photo is from
Wikipedia
.
The town people had long pondered the question of whether it is possible to
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CS109: Eulerian Circuits
www.cs.bu.edu/~best/courses/cs109/modules/euleriancircuits/
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walk through the town using every bridge just once, and returning home at
the end.
In 1736,
Euler
solved the longstanding question by mapping the problem to
a graph problem, which we examine next.
2.
Review the terminology for graphs
Vertices (a.k.a. nodes)
Edges (Directed vs undirected and labeled vs not labeled)
Paths (and shortest paths for labeled graphs)
3.
Reduce the map of the town shown above to the undirected, unlabeled graph
below.
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 Spring '13
 AzerBestavros
 Königsberg, se s/c s109/module, s.bu.e du/~be st/c, s/c s109/module s/e, s109/module s/e ule, ia nc ir

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