Outerplanar partial cubes

Abstract

[en] The class of outerplanar graphs is minor-closed and can be characterized by two excluded minors: ${\mathbf{}}K_{4}$ and $K_{2,3}$ Partial cubes are a class of graphs with good metric properties and have two defined operations that transform a partial cube into a PC-minor. We will study the outerplanar partial cubes, which is a PC-minor-closed class. The main result is the characterization of the set of obstructions of the class of outerplanar partial cubes.