Let be a family of graphs, and let and be nonnegative integers. The -Covering problem asks whether for a graph and an integer , there exists a set of at most vertices in such that has no induced subgraph isomorphic to a graph in , where …
By a seminal result of Valiant, computing the permanent of (0, 1)-matrices is, in general, #P-hard. In 1913 Pólya asked for which (0, 1)-matrices A it is possible to change some signs such that the permanent of A equals the determinant of the resulting matrix. In 1975, Little showed these matrices to be exactly the …
A linear -graph is called a (3-)hypertree if there exists exactly one path between each pair of two distinct vertices. A linear -graph is called a Steiner triple system if each pair of two distinct vertices belong to a unique edge. A simple greedy algorithm shows that every -vertex Steiner triple system contains all …