I am working on a project at present involving graph analysis. I basically need to mathematically model trees inside my graph. How can this be done using Matroids?
What I am looking for
Please note that this question is very general and it is meant to be so because I just need an overview about matroids. What are they capable of? How can they describe trees in a graph, what properties. Can you provide me just some links or papers about this?
My aim is mainly centered in finding trees in a graph. So the objective is to locate those edges that constitute a tree in my graphs. I have experienced some mathematical classic concepts for this, but I got to know something about matroids as being algebraic structures able to locate trees, loops and other interesting elements in a graph. What I need to understand is just the community opinion about matroids for these purposes.
Are matroids good at describing and finding trees in graphs?
How is this description performed?
Where can I find good links that explain me how to build a matroid to describe a graph?
How do I look in a matroid for trees?