Sufficient conditions on the existence of factors in graphs involving minimum degree

Huicai Jia; Jing Lou

Czechoslovak Mathematical Journal (2024)

  • Volume: 74, Issue: 4, page 1299-1311
  • ISSN: 0011-4642

Abstract

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For a set { A , B , C , ... } of graphs, an { A , B , C , ... } -factor of a graph G is a spanning subgraph F of G , where each component of F is contained in { A , B , C , ... } . 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.

How to cite

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Jia, Huicai, and Lou, Jing. "Sufficient conditions on the existence of factors in graphs involving minimum degree." Czechoslovak Mathematical Journal 74.4 (2024): 1299-1311. <http://eudml.org/doc/299650>.

@article{Jia2024,
abstract = {For a set $\lbrace A, B, C, \ldots \rbrace $ of graphs, an $\lbrace A, B, C, \ldots \rbrace $-factor of a graph $G$ is a spanning subgraph $F$ of $G$, where each component of $F$ is contained in $\lbrace A, B, C, \ldots \rbrace $. 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 $\lbrace K_2, \lbrace C_k\rbrace \rbrace $-factor, respectively.},
author = {Jia, Huicai, Lou, Jing},
journal = {Czechoslovak Mathematical Journal},
keywords = {factor; $Q$-spectral radius; distance spectral radius; minimum degree},
language = {eng},
number = {4},
pages = {1299-1311},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Sufficient conditions on the existence of factors in graphs involving minimum degree},
url = {http://eudml.org/doc/299650},
volume = {74},
year = {2024},
}

TY - JOUR
AU - Jia, Huicai
AU - Lou, Jing
TI - Sufficient conditions on the existence of factors in graphs involving minimum degree
JO - Czechoslovak Mathematical Journal
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 74
IS - 4
SP - 1299
EP - 1311
AB - For a set $\lbrace A, B, C, \ldots \rbrace $ of graphs, an $\lbrace A, B, C, \ldots \rbrace $-factor of a graph $G$ is a spanning subgraph $F$ of $G$, where each component of $F$ is contained in $\lbrace A, B, C, \ldots \rbrace $. 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 $\lbrace K_2, \lbrace C_k\rbrace \rbrace $-factor, respectively.
LA - eng
KW - factor; $Q$-spectral radius; distance spectral radius; minimum degree
UR - http://eudml.org/doc/299650
ER -

References

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