Associate Professor of Mathematics Debra Boutin recently published a research article "Structure and Properties of Locally Outerplanar Graphs" in the Journal of Combinatorial Mathematics and Combinatorial Computing. Boutin's paper investigates graphs (network diagrams) that can be drawn in the plane with their vertices on a circle and which contain no short self-intersecting path.
She calls these locally outerplanar graphs. One can easily build locally outerplanar graphs out of graphs that have no crossing edges. Boutin proves that every locally outerplanar graph arises from a construction of that type. This work builds on a previous paper of Boutin's "Convex Geometric Graphs with No Short Self-Intersecting Paths."
