ChromaticNumber[g] gives the chromatic number of the graph, which is the fewest number of colors necessary to color the graph.

ChvatalGraph returns a smallest triangle-free, 4-regular, 4-chromatic graph.

CircularEmbedding[n] constructs a list of n points equally spaced on a circle. CircularEmbedding[g] embeds the vertices of g equally spaced on a circle.

CliqueQ[g, c] yields True if the list of vertices c defines a clique in graph g.

Cofactor[m, {i, j}] calculates the (i, j)\[Null]^th cofactor of matrix m.

CompleteBinaryTree[n] returns a complete binary tree on n vertices.

CompleteKaryTree[n, k] returns a complete k-ary tree on n vertices.

ConstructTableau[p] performs the bumping algorithm repeatedly on each element of permutation p, resulting in a distinct Young tableau.

Contract[g, {x, y}] gives the graph resulting from contracting the pair of vertices {x, y} of graph g.

CostOfPath[g, p] sums up the weights of the edges in graph g defined by the path p.