Toroidal Cartesian Products Where One Factor is 3-Connected
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913049502285824 |
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| author | Badgett, Elizabeth Millichap, Christian Noguchi, Kenta |
| author_facet | Badgett, Elizabeth Millichap, Christian Noguchi, Kenta |
| contents | In this paper, we show that if $G$ is $3$-connected, then the Cartesian product of graphs $G \square H$ embeds on the torus if and only if $G$ is outer-cylindrical and $H$ is a path on two vertices, $P_2$. As a by-product of our work, we also show that $K_{4} \square P_{3}$ has genus two. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_12354 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Toroidal Cartesian Products Where One Factor is 3-Connected Badgett, Elizabeth Millichap, Christian Noguchi, Kenta Combinatorics 05C10 In this paper, we show that if $G$ is $3$-connected, then the Cartesian product of graphs $G \square H$ embeds on the torus if and only if $G$ is outer-cylindrical and $H$ is a path on two vertices, $P_2$. As a by-product of our work, we also show that $K_{4} \square P_{3}$ has genus two. |
| title | Toroidal Cartesian Products Where One Factor is 3-Connected |
| topic | Combinatorics 05C10 |
| url | https://arxiv.org/abs/2509.12354 |