Clique spectral extremal problem on disjoint color-critical graphs

Changjiang Bu; Peiyan Wei; Haotian Zeng

Clique spectral extremal problem on disjoint color-critical graphs

Combinatorics 2026-07-15 v1

Authors: Changjiang Bu , Peiyan Wei , Haotian Zeng

Abstract

For a given graph $F$ , a graph $G$ is called $F$ -free if it does not contain $F$ as a subgraph. A graph is color-critical if deleting one of its edges decreases its chromatic number. Let $F_1, F_2, \cdots, F_t$ be $t$ disjoint color-critical graphs with chromatic number $r+1$ . For $2 \leq s \leq r$ and sufficiently large $n$ , we determine the unique extremal graph with the maximum $s$ -clique spectral radius among all $n$ -vertex $\bigcup_{i=1}^t F_i$ -free graphs.

Keywords

spectral extremal problem clique spectral radius color-critical graphs F-free graphs extremal graph theory

Cite

@article{arxiv.2607.13861,
  title  = {Clique spectral extremal problem on disjoint color-critical graphs},
  author = {Changjiang Bu and Peiyan Wei and Haotian Zeng},
  journal= {arXiv preprint arXiv:2607.13861},
  year   = {2026}
}