The reducibility of optimal 1-planar graphs
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866913617248518144 |
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| author | Zhang, Licheng Huang, Yuanqiu |
| author_facet | Zhang, Licheng Huang, Yuanqiu |
| contents | A graph is reducible if it is the lexicographic product of two smaller non-trivial graphs. It is well-known a 1-planar graph with $n ~(\ge3)$ vertices has at most $4n-8$ edges, and a graph $G$ with $n$ vertices is optimal if $G$ has exactly $4n-8$ edges. In this paper, we characterize the reducibility of optimal 1-planar graphs. This work is motivated by a problem posed by Bucko and Czap in 2015, which concerns determining the 1-planarity of the lexicographic product of a graph and two isolated vertices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_14733 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The reducibility of optimal 1-planar graphs Zhang, Licheng Huang, Yuanqiu Combinatorics 05C10 05C62 05C76 A graph is reducible if it is the lexicographic product of two smaller non-trivial graphs. It is well-known a 1-planar graph with $n ~(\ge3)$ vertices has at most $4n-8$ edges, and a graph $G$ with $n$ vertices is optimal if $G$ has exactly $4n-8$ edges. In this paper, we characterize the reducibility of optimal 1-planar graphs. This work is motivated by a problem posed by Bucko and Czap in 2015, which concerns determining the 1-planarity of the lexicographic product of a graph and two isolated vertices. |
| title | The reducibility of optimal 1-planar graphs |
| topic | Combinatorics 05C10 05C62 05C76 |
| url | https://arxiv.org/abs/2211.14733 |