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Dominating maximal outerplane graphs and Hamiltonian plane triangulations
[article]
2019
arXiv
pre-print
Let $G$ be a graph and $\gamma (G)$ denote the domination number of $G$, i.e. the cardinality of a smallest set of vertices $S$ such that every vertex of $G$ is either in $S$ or adjacent to a vertex in $S$. Matheson and Tarjan conjectured that a plane triangulation with a sufficiently large number $n$ of vertices has $\gamma(G)\le n/4$. Their conjecture remains unsettled. In the present paper, we show that: (1) a maximal outerplane graph with $n$ vertices has $\gamma(G)\le \lceil \frac{n+k}
arXiv:1903.02462v1
fatcat:4ededjdiqzepnbhqywrjfeay5q