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- W4310285393 abstract "We study upper bounds on the size of optimum locating-total dominating sets in graphs. A set $S$ of vertices of a graph $G$ is a locating-total dominating set if every vertex of $G$ has a neighbor in $S$, and if any two vertices outside $S$ have distinct neighborhoods within $S$. The smallest size of such a set is denoted by $gamma^L_t(G)$. It has been conjectured that $gamma^L_t(G)leqfrac{2n}{3}$ holds for every twin-free graph $G$ of order $n$ without isolated vertices. We prove that the conjecture holds for cobipartite graphs, split graphs, block graphs, subcubic graphs and outerplanar graphs." @default.
- W4310285393 created "2022-11-30" @default.
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- W4310285393 date "2022-11-25" @default.
- W4310285393 modified "2023-09-26" @default.
- W4310285393 title "Progress towards the two-thirds conjecture on locating-total dominating sets" @default.
- W4310285393 doi "https://doi.org/10.48550/arxiv.2211.14178" @default.
- W4310285393 hasPublicationYear "2022" @default.
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