On k-(total) limited packing in graphs
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910436190846976 |
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| author | Ahmadi, Azam Sadat Soltankhah, Nasrin |
| author_facet | Ahmadi, Azam Sadat Soltankhah, Nasrin |
| contents | A set $B\subseteq V(G)$ is called a $k$-total limited packing set in a graph $G$ if $|B\cap N(v)|\leq k$ for any vertex $v\in V(G)$. The $k$-total limited packing number $L_{k,t}(G)$ is the maximum cardinality of a $k$-total limited packing set in $G$. Here, we give some results on the $k$-total limited packing number of graphs emphasizing trees, especially when $k=2$. We also study the $2$-(total) limited packing number of some product graphs.
A $k$-limited packing partition ($k$LPP) of graph $G$ is a partition of $V(G)$ into $k$-limited packing sets. The minimum cardinality of a $k$LPP is called the $k$LPP number of $G$ and is denoted by $χ_{\times k}(G)$, and we obtain some results for this parameter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03237 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On k-(total) limited packing in graphs Ahmadi, Azam Sadat Soltankhah, Nasrin Combinatorics 05C05, 05C69, 05C76 A set $B\subseteq V(G)$ is called a $k$-total limited packing set in a graph $G$ if $|B\cap N(v)|\leq k$ for any vertex $v\in V(G)$. The $k$-total limited packing number $L_{k,t}(G)$ is the maximum cardinality of a $k$-total limited packing set in $G$. Here, we give some results on the $k$-total limited packing number of graphs emphasizing trees, especially when $k=2$. We also study the $2$-(total) limited packing number of some product graphs. A $k$-limited packing partition ($k$LPP) of graph $G$ is a partition of $V(G)$ into $k$-limited packing sets. The minimum cardinality of a $k$LPP is called the $k$LPP number of $G$ and is denoted by $χ_{\times k}(G)$, and we obtain some results for this parameter. |
| title | On k-(total) limited packing in graphs |
| topic | Combinatorics 05C05, 05C69, 05C76 |
| url | https://arxiv.org/abs/2405.03237 |