Planar Turán numbers of cubic graphs and disjoint union of cycles

2022/02/18 by Yongxin Lan, Yongtang Shi, Lan, Yongxin +3 · 2 citations
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2202.09216

openalex publication_date 2022/02/18 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

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. In this paper, we study ex_P(n,H) when H is a cubic graph or disjoint union of cycles or H=K_{s, t}.

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