CS109_ Eulerian Circuits

Maketheobservationthatforacircuitthattraverseseveryedg

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Unformatted text preview: pt of a circuit ­­ a path that starts in a node and ends in the same node ­­ possibly going through nodes multiple times. 4. The question of the town of Konigsberg was to find a circuit that traverses every edge exactly once. Make the observation that for a circuit that traverses every edge exactly once to exist, every node must be entered and exited an equal number of times, and since no edge can be used twice, the node degree must be even. www.c s.bu.e du/~be st/c our se s/c s109/module s/e ule r ia nc ir c uits/ 2/4 2/10/14 CS109: Eule r ia n Cir c uits This suggest the following conj ecture. Conjecture: It is impossible to find a circuit that traverses all edges in a graph exactly once unless all nodes have an even degree. Proof: By contradiction. Since nodes A...
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