CS109_ Eulerian Circuits


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Unformatted text preview: , B, C, and D have odd degrees, it is obvious that this cannot be done in the above graph ­­ putting the question of the town of Konigsberg to rest. 5. Now we ask the following question: If a connected graph satisfies the condition that all its nodes have even degree, are we guaranteed the existence of a circuit that traverses every edge exactly once? For example, to carry the story of the town of Konigsberg further, upon discovery of the above theorem (that an even degree for all nodes is a necessary condition for Eulerian circuits to exist), the town demolished the bridge from A to D and built two new bridges from C to d and from B to D, as shown below. Now, as it turns out, it is possible indeed to cross every bridge exactly once and end up back where we started. Example: A g C e D d C f A a B c D B b A. Trying this on a number of small graphs, one will realize that this is...
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This note was uploaded on 02/10/2014 for the course CS 109 taught by Professor Azerbestavros during the Spring '13 term at BU.

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