2021/12/24 by Xiao‐Chuan Liu, Liu, Xiao-Chuan, Danni Peng +3
Mathematics · Social Sciences · #Limits and Structures in Graph Theory #Graph theory and applications #Political and Social Issues
paper · pdf · doi:10.48550/arxiv.2112.13119
In this paper, we investigate the Turán exponent for 1-subdivisions of graphs that are neither bipartite nor complete. Specifically, we establish an upper bound on the Turán number of the 1-subdivision of Ks,t+, where Ks,t+ is obtained by adding a single edge within the part of size s of the complete bipartite graph Ks,t, with 4≤ s ≤ t. In addition, we derive an upper bound for the extremal number of a family of graphs formed by (possibly degenerate) 1-subdivisions of certain tripartite graphs.