The density of maximal IC-plane graphs and maximal NIC-plane graphs
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911341772537856 |
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| author | Ding, Zongpeng Huang, Yuanqiu Dong, Fengming Lv, Shengxiang Gehér, Panna |
| author_facet | Ding, Zongpeng Huang, Yuanqiu Dong, Fengming Lv, Shengxiang Gehér, Panna |
| contents | In this paper, we show that any maximal IC-plane graph of order $n$ has at least $\left\lceil\frac{7}{3}n-\frac{14}{3}\right\rceil$ edges, and any maximal NIC-plane graph of order $n$ has at least $\left\lceil\frac{11}{5}n-\frac{18}{5}\right\rceil$ edges. Moreover, we show that both results are tight for infinitely many integers $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10218 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The density of maximal IC-plane graphs and maximal NIC-plane graphs Ding, Zongpeng Huang, Yuanqiu Dong, Fengming Lv, Shengxiang Gehér, Panna Combinatorics In this paper, we show that any maximal IC-plane graph of order $n$ has at least $\left\lceil\frac{7}{3}n-\frac{14}{3}\right\rceil$ edges, and any maximal NIC-plane graph of order $n$ has at least $\left\lceil\frac{11}{5}n-\frac{18}{5}\right\rceil$ edges. Moreover, we show that both results are tight for infinitely many integers $n$. |
| title | The density of maximal IC-plane graphs and maximal NIC-plane graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2501.10218 |