BipartiteMatchingAndCover[g] takes a bipartite graph g and returns a matching with maximum weight along with the dual vertex cover. If the graph is not weighted, it is ...

BipartiteMatching[g] gives the list of edges associated with a maximum matching in bipartite graph g. If the graph is edge weighted, then the function returns a matching with ...

CoarserSetPartitionQ[a, b] yields True if set partition b is coarser than set partition a; that is, every block in a is contained in some block in b.

CompleteQ[g] yields True if graph g is complete. This means that between any pair of vertices there is an undirected edge or two directed edges going in opposite directions.

DeleteCycle[g, c] deletes a simple cycle c from graph g. c is specified as a sequence of vertices in which the first and last vertices are identical. g can be directed or ...

DominatingIntegerPartitionQ[a, b] yields True if integer partition a dominates integer partition b, that is, the sum of a size-t prefix of a is no smaller than the sum of a ...

EquivalenceRelationQ[r] yields True if the matrix r defines an equivalence relation. EquivalenceRelationQ[g] tests whether the adjacency matrix of graph g defines an ...

EulerianQ[g] yields True if graph g is Eulerian, meaning there exists a tour that includes each edge exactly once.

GraphicQ[s] yields True if the list of integers s is a graphic sequence, and thus represents a degree sequence of some graph.

HamiltonianCycle[g] finds a Hamiltonian cycle in graph g if one exists. HamiltonianCycle[g, All] gives all Hamiltonian cycles of graph g.