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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.22660 |
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| _version_ | 1866914173572612096 |
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| author | Buahong, Siraphob Kittipassorn, Teeradej Nanta, Jiratchaphat Sripratak, Piyashat Suriya, Peerawit |
| author_facet | Buahong, Siraphob Kittipassorn, Teeradej Nanta, Jiratchaphat Sripratak, Piyashat Suriya, Peerawit |
| contents | We consider a graph representation in the plane, called the transparent rectangle visibility graph (TRVG), where each vertex is represented by a rectangle in the plane with sides parallel to the plane axes, in a way that any two vertices are adjacent if and only if a vertical or horizontal line can be drawn from the interior of one rectangle to the other. Expanding upon previously done work by Juntarapomdach and Kittipassorn, we show that $K_{3,3,3}$ is not a TRVG, and classify complete $k$-partite TRVGs. We also prove that the complement of $C^2_n$ is not a TRVG whenever $n \geq 15$, and that every $k$-partite TRVG with $n$ vertices has at most $2(k-1)n-k(k-1)$ edges. Furthermore, we introduce a novel representation, the intersecting transparent rectangle visibility graph (ITRVG), and show that there exists a graph that is an ITRVG but not a TRVG. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22660 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multipartite and Structural Results on Transparent Rectangle Visibility Graphs Buahong, Siraphob Kittipassorn, Teeradej Nanta, Jiratchaphat Sripratak, Piyashat Suriya, Peerawit Combinatorics 05C62 We consider a graph representation in the plane, called the transparent rectangle visibility graph (TRVG), where each vertex is represented by a rectangle in the plane with sides parallel to the plane axes, in a way that any two vertices are adjacent if and only if a vertical or horizontal line can be drawn from the interior of one rectangle to the other. Expanding upon previously done work by Juntarapomdach and Kittipassorn, we show that $K_{3,3,3}$ is not a TRVG, and classify complete $k$-partite TRVGs. We also prove that the complement of $C^2_n$ is not a TRVG whenever $n \geq 15$, and that every $k$-partite TRVG with $n$ vertices has at most $2(k-1)n-k(k-1)$ edges. Furthermore, we introduce a novel representation, the intersecting transparent rectangle visibility graph (ITRVG), and show that there exists a graph that is an ITRVG but not a TRVG. |
| title | Multipartite and Structural Results on Transparent Rectangle Visibility Graphs |
| topic | Combinatorics 05C62 |
| url | https://arxiv.org/abs/2511.22660 |