I am currently struggling with matchings in graph theory. I was wondering if someone could show me the proof/argument or explanation on how to solve it. Here is a picture of the triple flyswat graph
Here is what I do know: The graph contains bridges. So is that a reason it fails having a perfect matching?
There are an even number of vertices so that condition holds but when sketching the graph I notice the condition that every vertex being m-saturated fails.
I start marking matchings in one of the so called "Flyswatters?" Once I get to next flyswatter I see one vertex that is not saturated.