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- W4286815376 abstract "Several domination results have been obtained for maximal outerplanar graphs (mops). The classical domination problem is to minimize the size of a set $S$ of vertices of an $n$-vertex graph $G$ such that $G - N[S]$, the graph obtained by deleting the closed neighborhood of $S$, is null. A classical result of Chv'{a}tal is that the minimum size is at most $n/3$ if $G$ is a mop. Here we consider a modification by allowing $G - N[S]$ to have isolated vertices and isolated edges only. Let $iota_1(G)$ denote the size of a smallest set $S$ for which this is achieved. We show that if $G$ is a mop on $n geq 5$ vertices, then $iota_{1}(G) leq n/5$. We also show that if $n_2$ is the number of vertices of degree $2$, then $iota_{1}(G) leq frac{n+n_2}{6}$ if $n_2 leq frac{n}{3}$, and $iota_1(G) leq frac{n-n_2}{3}$ otherwise. We show that these bounds are best possible." @default.
- W4286815376 created "2022-07-24" @default.
- W4286815376 creator A5038574319 @default.
- W4286815376 creator A5063177210 @default.
- W4286815376 date "2019-03-28" @default.
- W4286815376 modified "2023-09-28" @default.
- W4286815376 title "Partial domination of maximal outerplanar graphs" @default.
- W4286815376 doi "https://doi.org/10.48550/arxiv.1903.12292" @default.
- W4286815376 hasPublicationYear "2019" @default.
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