The Maximum Number of Pentagons in a Planar Graph
Combinatorics
2022-12-06 v2
Abstract
In 1979, Hakimi and Schmeichel considered the problem of maximizing the number of cycles of a given length in an -vertex planar graph. They precisely determined the maximum number of triangles and -cycles and presented a conjecture for the maximum number of pentagons. In this work, we confirm their conjecture. Even more, we characterize the -vertex, planar graphs with the maximum number of pentagons.
Cite
@article{arxiv.1909.13532,
title = {The Maximum Number of Pentagons in a Planar Graph},
author = {Ervin Győri and Addisu Paulos and Nika Salia and Casey Tompkins and Oscar Zamora},
journal= {arXiv preprint arXiv:1909.13532},
year = {2022}
}