Demonstrating the tightness of the vertex label bound in Lemma 35. (A) A history graph with 5 labeled vertices. (B) A G-bounded AVG extension of the graph in (A) with 8 extra labeled vertices, the maximum possible. As only the leaf labels have the given label colour their labels are G-irreducible, all the other labels in the graph are bridges or junctions. For each extra labeled leaf vertex added to (A) an extra pair of junction and bridge adjacencies can be added to (B), thus the bound is tight for all m.