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 ...

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 ...

EdgeColoring[g] uses Brelaz's heuristic to find a good, but not necessarily minimal, edge coloring of graph g.

EdgeDirection is an option that takes on values True or False allowing the user to specify whether the graph is directed or not. EdgeDirection can be set as part of the graph ...

IdenticalQ[g, h] yields True if graphs g and h have identical edge lists, even though the associated graphics information need not be the same.

MeredithGraph returns a 4-regular, 4-connected graph that is not Hamiltonian, providing a counterexample to a conjecture by C. St. J. A. Nash\[Dash]Williams.

RGFToSetPartition[rgf, set] converts the restricted growth function rgf into the corresponding set partition of set.

SetPartitionToRGF[sp, set] converts the set partition sp of set into the corresponding restricted growth function.

Strings[l, n] constructs all possible combinatorial strings of length n from the elements of list l.

Turan[n, p] constructs the Turán graph, the extremal graph on n vertices that does not contain CompleteGraph[p].