Planarity of Mycielski-like graph expansions
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916737108148224 |
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| author | Vimal, Devansh |
| author_facet | Vimal, Devansh |
| contents | For a graph $G$, we define its great shadow $S(G)$ as a construction that duplicates each vertex $v$ in $G$ and sets this duplicated vertex adjacent to $v$ and all neighbors of $v$. Great graph shadows arise naturally in the routing of diode-and-switch circuits for computer keyboards, and are closely related to the Mycielski operation. These diode-and-switch circuits can be routed on a single-sided printed-circuit board if and only if the corresponding great shadow is planar. In this paper, we characterize all graphs with planar great shadows. Such graphs are always bipartite cactus graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_09534 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Planarity of Mycielski-like graph expansions Vimal, Devansh Combinatorics For a graph $G$, we define its great shadow $S(G)$ as a construction that duplicates each vertex $v$ in $G$ and sets this duplicated vertex adjacent to $v$ and all neighbors of $v$. Great graph shadows arise naturally in the routing of diode-and-switch circuits for computer keyboards, and are closely related to the Mycielski operation. These diode-and-switch circuits can be routed on a single-sided printed-circuit board if and only if the corresponding great shadow is planar. In this paper, we characterize all graphs with planar great shadows. Such graphs are always bipartite cactus graphs. |
| title | Planarity of Mycielski-like graph expansions |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2505.09534 |