English

The Planar Tur\'an Number of $\Theta_6$-graphs

Combinatorics 2024-07-01 v1

Abstract

There are two particular Θ6\Theta_6-graphs - the 6-cycle graphs with a diagonal. We find the planar Tur\'an number of each of them, i.e. the maximum number of edges in a planar graph GG of nn vertices not containing the given Θ6\Theta_6 as a subgraph and we find infinitely many extremal constructions showing the sharpness of these results - apart from a small additive constant error in one of the cases.

Keywords

Cite

@article{arxiv.2406.19584,
  title  = {The Planar Tur\'an Number of $\Theta_6$-graphs},
  author = {David Guan and Ervin Győri and Diep Luong-Le and Felicia Wang and Mengyuan Yang},
  journal= {arXiv preprint arXiv:2406.19584},
  year   = {2024}
}