Geodesic
Sufficient conditions on the existence of factors in graphs involving minimum degree
Czechoslovak Mathematical Journal, Tome 74 (2024) no. 4, pp. 1299-1311
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For a set $\{A, B, C, \ldots \}$ of graphs, an $\{A, B, C, \ldots \}$-factor of a graph $G$ is a spanning subgraph $F$ of $G$, where each component of $F$ is contained in $\{A, B, C, \ldots \}$. It is very interesting to investigate the existence of factors in a graph with given minimum degree from the prospective of eigenvalues. We first propose a tight sufficient condition in terms of the $Q$-spectral radius for a graph involving minimum degree to contain a star factor. Moreover, we also present tight sufficient conditions based on the $Q$-spectral radius and the distance spectral radius for a graph involving minimum degree to guarantee the existence of a $\{K_2, \{C_k\}\}$-factor, respectively.
For a set $\{A, B, C, \ldots \}$ of graphs, an $\{A, B, C, \ldots \}$-factor of a graph $G$ is a spanning subgraph $F$ of $G$, where each component of $F$ is contained in $\{A, B, C, \ldots \}$. It is very interesting to investigate the existence of factors in a graph with given minimum degree from the prospective of eigenvalues. We first propose a tight sufficient condition in terms of the $Q$-spectral radius for a graph involving minimum degree to contain a star factor. Moreover, we also present tight sufficient conditions based on the $Q$-spectral radius and the distance spectral radius for a graph involving minimum degree to guarantee the existence of a $\{K_2, \{C_k\}\}$-factor, respectively.
DOI : 10.21136/CMJ.2024.0304-24
Classification : 05C35, 05C50
Keywords: factor; $Q$-spectral radius; distance spectral radius; minimum degree 
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Jia, Huicai; Lou, Jing. Sufficient conditions on the existence of factors in graphs involving minimum degree. Czechoslovak Mathematical Journal, Tome 74 (2024) no. 4, pp. 1299-1311. doi: 10.21136/CMJ.2024.0304-24

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