An impossibility result on graph secret sharing (Q1039271)

Beginning with an overview of the secret sharing, the entropy method, and the multi-linear schemes the author defines a family of graphs \(G_2,G_3,\dots\) and compute \(k(G_i)\) for all members of the graph family. Further, the author presents schemes with slightly worse ratio than the bounds obtained earlier by the author in this paper. A novel construction for \(G_3\) has been provided which matches the lower bound; finally shown that there exists no similar construction which would work for \(G_4\) and consequently for other graphs in this family: any secret sharing scheme for \(G_n\) based on linear construction must have a strictly larger ratio than the entropy method gives.