Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 11 3 2026 09 01 On $k$-(total) limited packing in graphs 995 1011 14888 10.22049/cco.2025.29709.2125 EN Azam Sadat Ahmadi Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran Nasrin Soltankhah Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran Journal Article 2024 05 06 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. <br /><br /><br /><br />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 $\chi_{\times k}(G)$, and we obtain some results for this parameter. https://comb-opt.azaruniv.ac.ir/article_14888_0aa580287ee727be161ab97a0477d721.pdf