Minimum Number of Edges Guaranteeing the Existence of a $K_{1, t}$-Factor in a Graph
Minimum Number of Edges Guaranteeing the Existence of a $K_{1, t}$-Factor in a Graph
复制标题
保证图中 $K_{1, t}$ 因子存在的最小边数
DOI：
10.1007/s00373-023-02616-0
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发表时间：
2023
影响因子：
0.7
通讯作者：
Shinya Fujita
中科院分区：
文献类型：
--
作者：
Shuya Chiba;Yoshimi Egawa;Shinya Fujita
Lett,k,dbe integers withand, and let. We show that ifGis a graph of ordernsuch thatand \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|E(G)| \ge \left( {\begin{array}{c}n\\ 2\end{array}}\right) - (d + 1)n + dt + \frac{1}{2}(d^{2} + 3d + 4)$$\end{document}, thenGhas a-factor. We also give a construction showing the sharpness of the condition on |E(G)|.
Lett,k,dbe integers withand, and let. We show that ifGis a graph of ordernsuch thatand \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|E(G)| \ge \left( {\begin{array}{c}n\\ 2\end{array}}\right) - (d + 1)n + dt + \frac{1}{2}(d^{2} + 3d + 4)$$\end{document}, thenGhas a-factor. We also give a construction showing the sharpness of the condition on |E(G)|.