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This is a Quantitative Study study.

September 30, 2025Open Access

Projective Planar Cartesian Products of Graphs

Key Points

Only six forbidden minors are sufficient to classify projective planar Cartesian products, improving understanding of graph embeddings.
This research shows specific constraints for nonprojective planar graphs while organizing their essential properties.
The classification simplifies the understanding of Cartesian products with respect to their projective planar embeddings.
By constructing embeddings, this work lays a foundation for future studies in graph properties and planar classifications.

Abstract

In this paper, we provide a complete classification of Cartesian products of graphs that embed in the projective plane. Our work requires us to determine minimal Cartesian products that are nonprojective planar, organize their essential properties to be used as constraints for projective planar embeddings, and explicitly construct projective planar embeddings for Cartesian products that satisfy these constraints. A corollary of our work shows that only six of the 35 forbidden minors for the projective plane are sufficient to classify projective planar Cartesian products.

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Cite This Study

Abell et al. (Fri,) studied this question.

synapsesocial.com/papers/68dc1e358a7d58c25ebb17bf https://doi.org/https://doi.org/10.48550/arxiv.2509.10261

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