Explicit construction of linear sized tolerant networks

N. Alon, F.R.K. Chung
2006 Discrete Mathematics  
For every > 0 and every integer m > 0, we construct explicitly graphs with O(m/ ) vertices and maximum degree O(1/ 2 ), such that after removing any (1 − ) portion of their vertices or edges, the remaining graph still contains a path of length m. This settles a problem of Rosenberg, which was motivated by the study of fault tolerant linear arrays.
doi:10.1016/j.disc.2006.03.025 fatcat:sbp4m3smcbccxkrvvyplfuhfla