Show that the set of edges of a simple graph can be partitioned into cycles if a

Question

Show that the set of edges of a simple graph can be partitioned into cycles if and only if every vertex has an even degree. (In such a partition, each edge belongs to exactly one cycle.) Next argue that it is possible to orient the edges of a simple graph, in such a way that for each node its in-degree equals its out-degree, if and only if every vertex has an even degree. (An orientation of edges replaces each edge {x, y} by one of the two directed edges x y and y x.)

Hint: Consider a walk through the graph. As you stroll, you visit a node: first you enter this node via some edge, and then you leave it via some other edge. So you traversed two edges for this visit, unless it was a node from which you started. What if you enter an already visited node?

Please show each step you go through so I can learn from it. Thank you.

This is Discrete Structures class.

Explanation / Answer

hello sorry for inconvinience there is a ppt which clearly explains your requirement i will provide thi link please go through it

link:

https://www.google.co.in/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahUKEwiEj5Sb7uDLAhVNkI4KHY1NAD0QFggbMAA&url=http%3A%2F%2Fwww.cse.iitd.ernet.in%2F~Naveen%2Fcourses%2FCSL105%2Fslides%2Fgraphs.pptx&usg=AFQjCNENuXQ-yfhRmnyG2L4wUdLKU-HSNA&sig2=buMgpG6wY0Y8Kf6gypKLVw&bvm=bv.117868183,d.c2E

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