Question about a definition in Rivasseau's book

[Iliody]

I have a problem understanding a definition at page 93 of 'from perturbative to constructive renormalization', that is related to Graph Theory, and he uses it on the proof of the uniform BPH theorem for [itex]\phi_4^4[/itex] ([itex]\lambda \phi^4[/itex] in [itex]D=4[/itex]).
You have a graph G, a forest of quadrupeds F, and g a subgraph of G compatible with the tree structure of F. [itex]B_F(g)[/itex] is defined as the ancestor of g in FUG. What means ancestor in this context?
Maybe this question doesn't belong here, I'm sorry if that's the case. I thought that it belonged here because it's related to renormalization.

 

[LightHero]

Ancestor in this context means the graph obtained from $g$ by adding all the edges and vertices of the tree structure F which are not already present in $g$.