Projective Planar Cartesian Products of Graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914033547870208 |
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| author | Abell, Nicholas McDermott, Elizabeth Millichap, Christian |
| author_facet | Abell, Nicholas McDermott, Elizabeth Millichap, Christian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_10261 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Projective Planar Cartesian Products of Graphs Abell, Nicholas McDermott, Elizabeth Millichap, Christian Combinatorics 05C10, 05C83 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. |
| title | Projective Planar Cartesian Products of Graphs |
| topic | Combinatorics 05C10, 05C83 |
| url | https://arxiv.org/abs/2509.10261 |