I'm practicing for a math challenge and was asked whether the following graph has a perfect matching. I've tried to randomly connect nodes but couldn't find a way to connect the node in such a way that would result in a perfect matching, so I'm assuming it is not possibile.
But how do I know that it's really not possible? Is there a quicker (structured) way to determine whether there is a perfect matching or not, and how?
I only figured out that the number of nodes should be even, which is true in this case as there are 42 nodes.