Combinatorics / CONCEPT

Elimination rankings and rooted clique forests

The universe u is arbitrary. IsPEO(G,ord) has exactly two fields: ord is injective, and for each v the set of neighbors u with ord(v) < ord(u) is a clique. RelativeSimplicial(G,S,z) means that for all distinct a,b in S, adjacency of z to a and b implies adjacency of a to b. Nonempty(S) means that S contains an element. EliminatesEveryFiniteSet(G) says that each nonempty finite set contains such a z. LaterIn(G,S,f,v) is exactly the set of u in S with f(v) < f(u) and G.Adj v u.