CS109_ Eulerian Circuits


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Unformatted text preview: always possible. But is it true for all possible graphs (satisfying the above condition)? For this we need to prove the following conj ecture: Conjecture: There exists a circuit that traverses every edge in a connected graph whose nodes are all of even degrees. Proof: By induction. www.c s.bu.e du/~be st/c our se s/c s109/module s/e ule r ia nc ir c uits/ 3/4 2/10/14 CS109: Eule r ia n Cir c uits Base: Show that this must be the case for the graph with the smallest number of nodes ­­ namely three nodes in a cycle. Step: Assume that the conj ecture holds for all graphs (connected with even­degree nodes) of size less than N nodes, and consider a graph of size N. Start in any node and follow an edge to another node. Since nodes have even degrees, I am guarantee...
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