A characterization of the edge-shelling convex geometries of trees

TL;DR

This paper characterizes the class of convex geometries derived from the edge-sets of subtrees in trees, providing a forbidden minors characterization and exploring properties like closure under trace operations.

Contribution

It offers a complete characterization of edge-shelling convex geometries of trees using trace-minimal forbidden minors, advancing understanding of their structural properties.

Findings

The size of the stem of any rooted circuit is two.

The class is closed under trace operation.

Forbidden minors are specified for the class.

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.