[Math] Can a connected Eulerian graph have an even number of vertices and an odd number of edges

discrete mathematicseulerian-pathgraph theory

I know that the requirements for a Eulerian graph are that all vertex degrees are even and that it is connected. But I am not sure how that would work with the amount of vertices and edges.

So, if this is possible, how would we draw a graph like that? If it isn't possible, how can we prove that?

Thank you!

Best Answer

Edit: Sorry, my previous answer was incorrect.

In fact, there is such a graph. Consider a hexagon with a triangle inside: enter image description here

Related Question