Geodesic
Computational complexity of graph extensions
Prikladnaâ diskretnaâ matematika, no. 10 (2009), pp. 94-95 
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/
@article{PDM_2009_10_a47,
     author = {M. B. Abrosimov},
     title = {Computational complexity of graph extensions},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {94--95},
     year = {2009},
     number = {10},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2009_10_a47/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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 $G$?".

[1] Hayes J. P., “A graph model for fault-tolerant computing system”, IEEE Trans. Comput., 25:9 (1976), 875–884 | DOI | MR | Zbl

[2] Harary F., Hayes J. P., “Edge fault tolerance in graphs”, Networks, 23 (1993), 135–142 | DOI | MR | Zbl

[3] Harary F., Hayes J. P., “Node fault tolerance in graphs”, Networks, 27 (1996), 19–23 | 3.0.CO;2-H class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[4] Abrosimov M. B., “Minimalnye rasshireniya grafov”, Novye informatsionnye tekhnologii v issledovanii diskretnykh struktur, Tomsk, 2008, 59–64