CS109_ Eulerian Circuits

Stepassumethattheconj

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

Ask a homework question - tutors are online