Hello,
I'm afraid that I've suddenly become of those people who really used to annoy me when I tried to help them, because I had my first lesson on graphs and matching today in Further Maths, and I don't understand any of it. The entire concept escapes me, even though there doesn't seem to be anything complicated involved. My teacher has tried multiple times to help me, and I've looked up definitions for myself, but it still just feels like reading words and not understanding a thing. Could anyone please explain and define matching, maximal matching, maximum matching and perfect matching for me, in very simple language?
As an example, here is a definition that doesn't mean anything to me: "A maximal matching is a matching M of a graph G with the property that if any edge not in M is added to M, it is no longer a matching, that is, M is maximal if it is not a proper subset of any other matching in graph G. In other words, a matching M of a graph G is maximal if every edge in G has a non-empty intersection with at least one edge in M."
Sorry for the long post, but I'm trying to make the questions as clear as possible.
Thanks.
TL;DR Could anyone please explain and define matching, maximal matching, maximum matching and perfect matching for me, in very simple language?