Spectral condition for $k$-factor-criticality in $t$-connected graphs

Tingyan Ma; Edwin R. van Dam; Ligong Wang

Spectral condition for $k$-factor-criticality in $t$-connected graphs

Combinatorics 2025-09-03 v5

Authors: Tingyan Ma , Edwin R. van Dam , Ligong Wang

Abstract

A graph $G$ is called $k$ -factor-critical if $G-S$ has a perfect matching for every $S\subseteq G$ with $|S|=k$ . A connected graph $G$ is called $t$ -connected if it has more than $t$ vertices and remains connected whenever fewer than $t$ vertices are removed. We give a condition on the number of edges and a condition on the spectral radius for $k$ -factor-criticality in $t$ -connected graphs.

Keywords

rainbow connection graph connectivity graph theory

Cite

@article{arxiv.2503.22951,
  title  = {Spectral condition for $k$-factor-criticality in $t$-connected graphs},
  author = {Tingyan Ma and Edwin R. van Dam and Ligong Wang},
  journal= {arXiv preprint arXiv:2503.22951},
  year   = {2025}
}

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