This preview shows page 1. Sign up to view the full content.
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
 Spring '13
 AzerBestavros

Click to edit the document details