Spectral radius and k-factor-critical graphsSpectral radius and k-factor-critical graphsS. Zhou et al.

被引：0

作者：

Sizhong Zhou ^{[1
]}

Zhiren Sun ^{[2
]}

Yuli Zhang ^{[3
]}

机构：

[1] Jiangsu University of Science and Technology,School of Science

[2] Nanjing Normal University,School of Mathematical Sciences

[3] Dalian Jiaotong University,School of Science

来源：

The Journal of Supercomputing | / 81卷 / 3期

关键词：

Graph; Spectral radius; Perfect matching; -factor-critical graph; 05C50; 05C70;

D O I：

10.1007/s11227-024-06902-3

中图分类号：

学科分类号：

摘要：

For a nonnegative integer k, a graph G is said to be k-factor-critical if G-Q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G-Q$$\end{document} admits a perfect matching for any Q⊆V(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Q\subseteq V(G)$$\end{document} with |Q|=k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|Q|=k$$\end{document}. In this article, we prove spectral radius conditions for the existence of k-factor-critical graphs. Our result generalizes one previous result on perfect matchings of graphs. Furthermore, we claim that the bounds on spectral radius in Theorem 3.1 are sharp.

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