PerfectQ[g] yields True if g is a perfect graph, meaning that for every induced subgraph of g the size of a largest clique equals the chromatic number.

PermutationWithCycle[n, {i, j, ...}] gives a size-n permutation in which {i, j, ...} is a cycle and all other elements are fixed points.

PermuteSubgraph[g, p] permutes the vertices of a subgraph of g induced by p according to p.

PetersenGraph returns the Petersen graph, a graph whose vertices can be viewed as the size-2 subsets of a size-5 set with edges connecting disjoint subsets.

RandomKSetPartition[set, k] returns a random set partition of set with k blocks. RandomKSetPartition[n, k] returns a random set partition of the first n natural numbers into ...

RandomRGF[n] returns a random restricted growth function (RGF) defined on the first n natural numbers. RandomRGF[n, k] returns a random RGF defined on the first n natural ...

RandomSetPartition[set] returns a random set partition of set. RandomSetPartition[n] returns a random set partition of the first n natural numbers.

RandomSubset[l] creates a random subset of set l.

RankBinarySubset[l, s] gives the rank of subset s of set l in the ordering of subsets of l, obtained by interpreting these subsets as binary string representations of ...

RankGrayCodeSubset[l, s] gives the rank of subset s of set l in the Gray code ordering of the subsets of l.