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Tur\'an Number of Subdivisions of Multipartite Graphs

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arxiv 2112.13119 v3 pith:2T5OCLVO submitted 2021-12-24 math.CO

Xiao-Chuan Liu , Danni Peng , Xu Yang This is my paper · ORCID
classification math.CO
keywords graphsnumbersubdivisionsbipartiteboundcompleteupperadding
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abstract

In this paper, we investigate the Tur\'an exponent for $1$-subdivisions of graphs that are neither bipartite nor complete. Specifically, we establish an upper bound on the Tur\'an number of the 1-subdivision of $K_{s,t}^+$, where $K_{s,t}^+$ is obtained by adding a single edge within the part of size $s$ of the complete bipartite graph $K_{s,t}$, with $4\leq s \leq t$. 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.

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Cited by 1 Pith paper

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  1. Linear Lower Bounds for the Modular Chromatic Index

    math.CO 2026-08 accept novelty 8.0 of 10

    Bipartite graphs force the mod-k chromatic index to grow as 3k/2, refuting the Botler–Colucci–Kohayakawa conjecture.

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