Excluded minor

An excluded minor is a specific type of graph that cannot contain a certain smaller graph as a part of it, no matter how you look at it. In the study of graph structures, mathematicians classify larger graphs based on the smaller "building block" graphs they avoid. If a graph doesn't contain a particular smaller graph as a subgraph, but all of its "simplifications" do, then that larger graph is considered an excluded minor for that property. These excluded minors help us understand the fundamental limits of certain graph classes and their structural properties.