MaximumClique[g] finds a largest clique in graph g. MaximumClique[g, k] returns a k-clique, if such a thing exists in g; otherwise it returns {}.

MaximumIndependentSet[g] finds a largest independent set of graph g.

MaximumSpanningTree[g] uses Kruskal's algorithm to find a maximum spanning tree of graph g.

McGeeGraph returns the unique (7, 3)-cage, a 3-regular graph with girth 7.

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.

MinimumChainPartition[g] partitions partial-order g into a minimum number of chains.

MinimumChangePermutations[l] constructs all permutations of list l such that adjacent permutations differ by only one transposition.

MinimumSpanningTree[g] uses Kruskal's algorithm to find a minimum spanning tree of graph g.

MinimumVertexColoring[g] returns a minimum vertex coloring of g. MinimumVertexColoring[g, k] returns a k-coloring of g, if one exists.

MinimumVertexCover[g] finds a minimum vertex cover of graph g.