Geodesic
Computational complexity of graph extensions
Prikladnaâ diskretnaâ matematika, no. 10 (2009), pp. 94-95

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A graph $G^*$ is $k$-vertex (edge) extension of graph $G$ if every graph obtained by removing any $k$ vertexes (edges) from $G^*$ contains $G$. We prove NP-completeness of the problem: "Is graph $G^*$ a $k$-vertex (edge) extension of graph $G$?". 
@article{PDM_2009_10_a47,
     author = {M. B. Abrosimov},
     title = {Computational complexity of graph extensions},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {94--95},
     publisher = {mathdoc},
     number = {10},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2009_10_a47/}
}
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M. B. Abrosimov. Computational complexity of graph extensions. Prikladnaâ diskretnaâ matematika, no. 10 (2009), pp. 94-95. http://geodesic.mathdoc.fr/item/PDM_2009_10_a47/