What are all the tricks that make a graph drawable? I know that a graph is drawable when you can draw the graph without lifting your pen off the paper and without retracing any edges. I know that if every vertex has even degree then it is Eulerian. I know that Eulerian graphs can have repeated vertices.
1) Can you ever have a connected graph with an odd number of vertices each with an odd degree? I've tried a lot of connected graphs and it looks like the answer is no.
2) Will a graph that is Eulerian always start and end on vertices of odd degree if the graph contains vertices of odd degree? Looks like it so far with all the Eulerian graphs I've constructed so far.
3) What are all the tricks for finding if a graph is Eulerian?