DOI: 10.1002/jgt.23008 ISSN: 0364-9024
The product structure of squaregraphs
Robert Hickingbotham, Paul Jungeblut, Laura Merker, David R. Wood- Geometry and Topology
- Discrete Mathematics and Combinatorics
Abstract
A squaregraph is a plane graph in which each internal face is a 4‐cycle and each internal vertex has degree at least 4. This paper proves that every squaregraph is isomorphic to a subgraph of the semistrong product of an outerplanar graph and a path. We generalise this result for infinite squaregraphs, and show that this is best possible in the sense that “outerplanar graph” cannot be replaced by “forest”.