| Minimum $k$-Path Vertex Cover in Cartesian Product Graphs |
| Received:November 27, 2020 Revised:April 07, 2021 |
| Key Words:
$k$-path vertex cover Cartesian product graphs bound
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.61463026; 61463027). |
| Author Name | Affiliation | | Huiling YIN | School of Mathematics and Physics, Lanzhou Jiaotong University, Gansu 730070, P. R. China | | Binbin HAO | School of Traffic and Transportation, Lanzhou Jiaotong University, Gansu 730070, P. R. China | | Xiaoyan SU | School of Mathematics and Physics, Lanzhou Jiaotong University, Gansu 730070, P. R. China | | Jingrong CHEN | School of Mathematics and Physics, Lanzhou Jiaotong University, Gansu 730070, P. R. China |
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| Abstract: |
| For the subset $S\subseteq V(G)$, if every path with $k$ vertices in a graph $G$ contains at least one vertex from $S$, we call that $S$ is a $k$-path vertex cover set of the graph $G$. Obviously, the subset is not unique. The cardinality of the minimum $k$-path vertex cover set of a graph $G$ is called the $k$-path vertex cover number, we denote it by $\psi_k(G)$. In this paper, a lower or upper bound of $\psi_k$ for some Cartesian product graphs is presented. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2021.04.002 |
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