Does this have a Euler circuit or a Euler path?

Question

Not quite sure on how to find the Euler path in here. If there's even one.

diagram

Do you know a relation between existence of such paths and degrees of vertices? — , Oct 11 '15 at 04:18
Possible duplicate of Is it possible to draw this picture without lifting the pen? — Ilmari Karonen, Jan 01 '16 at 17:13

score 3 · Answer 1 · answered Oct 11 '15 at 04:22

There is a standard method for checking whether a simple connected graph has an Eulerian Circuit. A simple connected graph has an Eulerian circuit iff the degree of every vertex is even. Then, you can just go ahead and on such a small graph construct one. For example, ABFECDEGCBGFA.

However, all you need for an Eulerian path is that at least n-2 vertices have even degree where n is the number of vertices in your graph. Then , you start at a vertex with odd degree and end at one as well.

Does this have a Euler circuit or a Euler path?

1 Answers1