A correction of a characterization of planar partial cubes

TL;DR

This paper identifies the specific expansions that characterize when a partial cube is planar, correcting a previous inaccurate result and providing a precise construction method.

Contribution

It precisely characterizes the expansions that generate all planar partial cubes from a single vertex, correcting earlier inaccuracies.

Findings

Identifies the set of expansions for planar partial cubes.

Provides a corrected characterization of planar partial cubes.

Clarifies the construction process from a single vertex.

Abstract

In this note we determine the set of expansions such that a partial cube is planar if and only if it arises by a sequence of such expansions from a single vertex. This corrects a result of Peterin.