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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/2503.13243 |
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| _version_ | 1866910878958354432 |
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| author | Hubard, Isabel Potočnik, Primož Šparl, Primož |
| author_facet | Hubard, Isabel Potočnik, Primož Šparl, Primož |
| contents | In this paper, we provide the first known infinite family of simple graphs, each of which is the skeleton of a chiral map, a skeleton of a reflexible map on an orientable surfaces, as well as a skeleton of a reflexible map on a non-orientable surface. This family consists of all lexicographic product $C_n[mK_1]$, where $m\ge 3$, $n = sm$, with $s$ an integer not divisible by $4$. This answers a question posed in [S.\ Wilson, Families of regular graphs in regular maps, {\em Journal of Combinatorial Theory, Series B} 85 (2002), 269--289]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_13243 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An infinite family of simple graphs underlying chiral, orientable reflexible and non-orientable rotary maps Hubard, Isabel Potočnik, Primož Šparl, Primož Combinatorics 05E18 In this paper, we provide the first known infinite family of simple graphs, each of which is the skeleton of a chiral map, a skeleton of a reflexible map on an orientable surfaces, as well as a skeleton of a reflexible map on a non-orientable surface. This family consists of all lexicographic product $C_n[mK_1]$, where $m\ge 3$, $n = sm$, with $s$ an integer not divisible by $4$. This answers a question posed in [S.\ Wilson, Families of regular graphs in regular maps, {\em Journal of Combinatorial Theory, Series B} 85 (2002), 269--289]. |
| title | An infinite family of simple graphs underlying chiral, orientable reflexible and non-orientable rotary maps |
| topic | Combinatorics 05E18 |
| url | https://arxiv.org/abs/2503.13243 |