The spectral radius of 1-planar graphs without complete subgraphs

2025/12/15 by Weilun Xu, Xu, Weilun, An Chang +1
Computer Science · Mathematics · #05C10 #05C50 #Advanced Graph Theory Research #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #G.2.2 #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.2512.12909

openalex publication_date 2025/12/15 · openalex created_date 2025/12/17 · openalex updated_date 2026/07/28

Abstract

A 1-planar graph refers to a graph that can be drawn on the plane such that each edge has at most one crossing. In this paper, focusing on the spectral Turán-type problems of 1-planar graphs, we determine completely the unique spectral extremal graph among all K₃-free or K₄-free 1-planar graphs, and provide a characterization of the spectral extremal graphs for K₅-free 1-planar graphs, confining the candidates to a specific, small family.

Citations

• The maximum spectral radius of planner graphs without the joint of K2 and a linear forest
• On the spectral extremal problem of planar graphs
• Extremal spectral results of planar graphs without vertex-disjoint cycles
• Extremal spectral results of planar graphs without vertex‐disjoint cycles
• Extremal problems on planar graphs without k edge-disjoint cycles
• On the sizes of bipartite 1-planar graphs
• Three conjectures in extremal spectral graph theory
• Bounds on graph eigenvalues II

Related

• On the spectral extremal problem of planar graphs
• Extremal spectral results of planar graphs without C_{l, l} or Theta graph
• Extremal spectral results of planar graphs without vertex‐disjoint cycles
• Spectral Extremal Graphs of Planar Graphs with Fixed Size
• Extremal spectral results of planar graphs without vertex-disjoint cycles