Say we have a graph with 6 nodes/vertices. Say that within this graph, we draw 12 edges connecting the nodes. Why can we guarantee that at least one of the nodes will have 3 edges connected to it?
I understand why this has to be true when drawn out on paper, but I am wondering if there is a principle or theory that could help in explaining this. I'd like to understand it from a mathematical perspective rather than pure intuition. Thanks!