Planar Turán number of two adjacent cycles

2024/11/27 by Song, Xinzhe, Qiang Zhou, Yan, Guiying +1
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2411.18487

openalex publication_date 2024/11/27 · openalex created_date 2024/12/05 · openalex updated_date 2026/07/30

Abstract

The planar Turán number of H, denoted by ex_P(n,H), is the maximum number of edges in an n-vertex H-free planar graph. The planar Turán number of k(k≥ 3) vertex-disjoint union of cycles is the trivial value 3n-6. We determine the planar Turán number of C₃-C₃ and C₃-C₄, where C_k-C_ℓ denotes the graph consisting of two disjoint cycles C_k with an edge connecting them.

Related

• Planar Turán number of disjoint union of C₃ and C₄
• Planar Turán number of disjoint union of C₃ and C₅
• Planar Turán numbers of cubic graphs and disjoint union of cycles
• Planar Turán numbers of three configurations
• An improved lower bound for the planar Turán number of cycles