Geodesic
On minimal edge $k$-extensions of oriented stars
Prikladnaâ diskretnaâ matematika, no. 12 (2010), pp. 67-68

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A graph $G^*$ is $k$-edge extension of graph $G$ if every graph obtained by removing any $k$ edges(arcs) from $G^*$ contains $G$. $k$-edge extension of graph $G$ with $n$ vertices is called minimal if among all $k$-edge extensions of graph $G$ with $n$ vertices it has the minimum possible number of edges (arcs). Oriented star is obtained from unoriented star by replacing edges with arcs. We provide the complete description of minimal $k$-edge extensions for oriented stars. 
@article{PDM_2010_12_a31,
     author = {M. B. Abrosimov},
     title = {On minimal edge $k$-extensions of oriented stars},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {67--68},
     publisher = {mathdoc},
     number = {12},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2010_12_a31/}
}
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M. B. Abrosimov. On minimal edge $k$-extensions of oriented stars. Prikladnaâ diskretnaâ matematika, no. 12 (2010), pp. 67-68. http://geodesic.mathdoc.fr/item/PDM_2010_12_a31/