English

The density of maximal IC-plane graphs and maximal NIC-plane graphs

Combinatorics 2025-12-30 v2

Abstract

In this paper, we show that any maximal IC-plane graph of order nn has at least 73n143\left\lceil\frac{7}{3}n-\frac{14}{3}\right\rceil edges, and any maximal NIC-plane graph of order nn has at least 115n185\left\lceil\frac{11}{5}n-\frac{18}{5}\right\rceil edges. Moreover, we show that both results are tight for infinitely many integers nn.

Keywords

Cite

@article{arxiv.2501.10218,
  title  = {The density of maximal IC-plane graphs and maximal NIC-plane graphs},
  author = {Zongpeng Ding and Yuanqiu Huang and Fengming Dong and Shengxiang Lv and Panna Gehér},
  journal= {arXiv preprint arXiv:2501.10218},
  year   = {2025}
}