Suppose to toss an independent coin with equal probability of success and failure for each subset of [n] = {1, 2, ..., n}, and form the random hypergraph H(n) by taking as hyperedges the subsets with successful coin t...Suppose to toss an independent coin with equal probability of success and failure for each subset of [n] = {1, 2, ..., n}, and form the random hypergraph H(n) by taking as hyperedges the subsets with successful coin tosses. It is proved that H(n) is almost surely connected. By defining a graph G(S) according to a subset system S, it is shown that the intersecting problem is NP-complete.展开更多
文摘Suppose to toss an independent coin with equal probability of success and failure for each subset of [n] = {1, 2, ..., n}, and form the random hypergraph H(n) by taking as hyperedges the subsets with successful coin tosses. It is proved that H(n) is almost surely connected. By defining a graph G(S) according to a subset system S, it is shown that the intersecting problem is NP-complete.
