A characterization of the edge-shelling convex geometries of trees
Abstract
We investigate the class of the edge-shelling convex geometries of trees. The edge-shelling convex geometry of a tree is the convex geometry consisting of the sets of edges of the subtrees. For the edge-shelling convex geometry of a tree, the size of the stem of any rooted circuit is two. The class of the edge-shelling convex geometry of a tree is closed under trace operation. We characterize the class of the edge-shelling convex geometry of a tree in terms of trace-minimal forbidden minors. Moreover, the trace-minimal forbidden minors are specified for the class of convex geometries such that the size of any stem is two.
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