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

David Guan; Diep Luong-Le; Ervin Gy\H{o}ri; Felicia Wang; Mengyuan Yang

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

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2406.19584 v1 pith:RRA4Y27A submitted 2024-06-28 math.CO

David Guan , Ervin Győri , Diep Luong-Le , Felicia Wang , Mengyuan Yang This is my paper · ORCID

classification math.CO

keywords graphsnumberplanarthetafindadditiveapartcases

verification ladder T0 review T1 audit T2 compute T3 formal

0 comments

abstract

There are two particular $\Theta_6$-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 $G$ of $n$ vertices not containing the given $\Theta_6$ 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.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Planar Tur\'an number of quasi-double stars
math.CO 2025-07 conditional novelty 5.0 of 10

For quasi-double stars W_{h,k} with 1≤h≤2≤k≤5, the paper proves planar Turán bounds of 3(h+k)/(h+k+2)n for h+k≤5, and two-sided bounds of 5/2 n and 17/6 n for larger cases.

Pith tools