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CS109_ Eulerian Circuits

# CS109_ Eulerian Circuits - CS109 Eule r ia n Cir c uits...

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2/10/14 CS109: Eulerian Circuits www.cs.bu.edu/~best/courses/cs109/modules/euleriancircuits/ 1/4 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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2/10/14 CS109: Eulerian Circuits www.cs.bu.edu/~best/courses/cs109/modules/euleriancircuits/ 2/4 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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CS109_ Eulerian Circuits - CS109 Eule r ia n Cir c uits...

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