Nearby in the stack

Planar Turán numbers of cubic graphs and disjoint union of cycles · arXivDesk

2202.09216Feb 18, 2022The second version adds an improved lower bound for the planar Turan number of disjoint union of cycles of length at least seven, see Lemma 5.2. arXiv admin note: text overlap with arXiv:1808.01487

Planar Turán numbers of cubic graphs and disjoint union of cycles

Yongxin Lan, Yongtang Shi, Zi-Xia Song

Combinatorics

arXiv PDF

Abstract

The planar Turán number of a graph $H$ , denoted $ex_{_\mathcal{P}}(n,H)$ , is the maximum number of edges in a planar graph on $n$

Briefing

What this paper is actually doing

This is a heuristic sketch from the abstract. Sign in for a live briefing.

The planar Turán number of a graph H, denoted ex__P(n,H), is the maximum number of edges in a planar graph on n vertices without containing H as a subgraph. This notion was introduced by Dowden in 2016 and has attracted quite some attention since then; those work mainly focus on finding ex__P(n,H) when H is a cycle or Theta graph or H has maximum degree at least four.

GraduateNovelty 3/5

Researchers working in math.CO and adjacent areas.

Claims

The paper addresses: Planar Turán numbers of cubic graphs and disjoint union of cycles.
The planar Turán number of a graph H, denoted ex__P(n,H), is the maximum number of edges in a planar graph on n vertices without containing H as a subgraph.

Methods

Method details are not extracted without an AI key — open the PDF or HTML version.
Author comment: The second version adds an improved lower bound for the planar Turan number of disjoint union of cycles of length at least seven, see Lemma 5.2. arXiv admin note: text overlap with arXiv:1808.01487

Limitations

This is a heuristic briefing generated without a language model. Treat it as a sketch, not an analysis.

Why it matters

Newly listed under math.CO. Connect your OpenRouter key to unlock a full arXivDesk briefing.

Open questions

What is the strongest empirical result, and on which baseline?
Which assumption would most change the conclusion if it failed?

Socratic margin

Ask the abstract

Questions are grounded in the title and abstract. If the PDF is required, arXivDesk will say so.

Nearby in the stack

arXiv did not return neighbours for this paper. Try again in a bit.