Geodesic
Number estimation for additional arcs in a~minimal $1$-vertex extension of tournament
Prikladnaya Diskretnaya Matematika. Supplement, no. 8 (2015), pp. 111-113

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We obtain lower and upper bounds for the number of additional arcs in minimal vertex $1$-extension of arbitrary tournament. It is shown that the estimates are sharp. We describe tournaments, for which estimates are attained.
Keywords: tournament, minimal vertex extension, fault-tolerance. 
@article{PDMA_2015_8_a41,
     author = {M. B. Abrosimov and O. V. Modenova},
     title = {Number estimation for additional arcs in a~minimal $1$-vertex extension of tournament},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {111--113},
     publisher = {mathdoc},
     number = {8},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2015_8_a41/}
}
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M. B. Abrosimov; O. V. Modenova. Number estimation for additional arcs in a~minimal $1$-vertex extension of tournament. Prikladnaya Diskretnaya Matematika. Supplement, no. 8 (2015), pp. 111-113. http://geodesic.mathdoc.fr/item/PDMA_2015_8_a41/