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- W2050574881 abstract "We study the graphs $G$ for which the hull number $h(G)$ and the geodetic number $g(G)$ with respect to $P_3$-convexity coincide. These two parameters correspond to the minimum cardinality of a set $U$ of vertices of $G$ such that the simple expansion process which iteratively adds to $U$ all vertices outside of $U$ having two neighbors in $U$ produces the whole vertex set of $G$ either eventually or after one iteration, respectively. We establish numerous structural properties of the graphs $G$ with $h(G)=g(G)$, allowing for the constructive characterization as well as the efficient recognition of all such graphs that are triangle-free. Furthermore, we characterize---in terms of forbidden induced subgraphs---the graphs $G$ that satisfy $h(G')=g(G')$ for every induced subgraph $G'$ of $G$." @default.
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- W2050574881 date "2013-01-01" @default.
- W2050574881 modified "2023-09-27" @default.
- W2050574881 title "Geodetic Number versus Hull Number in $P_3$-Convexity" @default.
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- W2050574881 doi "https://doi.org/10.1137/110859014" @default.
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