Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.04257 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- Given a graph family $\mathbb{H}$, let ${\rm SPEX}(n,\mathbb{H}_{\rm sub})$ denote the set of $n$-vertex $\mathbb{H}$-subdivision-free graphs with the maximum spectral radius. In this paper, we investigate the problem of graph subdivision from a spectral extremal perspective, with a focus on the structural characterization of graphs in ${\rm SPEX}(n,\mathbb{H}_{\rm sub})$. For any graph $H \in \mathbb{H}$, let $α(H)$ denote its independence number. Define $γ_\mathbb{H}:=\min_{H\in \mathbb{H}}\{|H| - α(H) - 1\}$. We prove that every graph in ${\rm SPEX}(n,\mathbb{H}_{\rm sub})$ contains a spanning subgraph isomorphic to $K_{γ_\mathbb{H}}\vee (n-γ_\mathbb{H})K_1$, which is obtained by joining a $γ_\mathbb{H}$-clique with an independent set of $n-γ_\mathbb{H}$ vertices. This extends a recent result by Zhai, Fang, and Lin concerning spectral extremal problems for $\mathbb{H}$-minor-free graphs.