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 ...

BrelazColoring[g] returns a vertex coloring in which vertices are greedily colored with the smallest available color in decreasing order of vertex degree.

ChromaticPolynomial[g, z] gives the chromatic polynomial P(z) of graph g, which counts the number of ways to color g with, at most, z colors.

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.

CodeToLabeledTree[l] constructs the unique labeled tree on n vertices from the Prüfer code l, which consists of a list of n - 2 integers between 1 and n.

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.

Compositions[n, k] gives a list of all compositions of integer n into k parts.

CoxeterGraph gives a non-Hamiltonian graph with a high degree of symmetry such that there is a graph automorphism taking any path of length 3 to any other.

CycleStructure[p, x] returns the monomial in x[1], x[2], ..., x[Length[p]] that is the cycle structure of the permutation p.

CyclicGroupIndex[n, x] returns the cycle index of the cyclic group on n symbols, expressed as a polynomial in x[1], x[2], ..., x[n].