# Undirected unweighted sub-graph enumeration with threshold on node value

I have an undirected, unweighted graph $$G=(V,E)$$, and a function $$f:V\to [0,1]$$ where $$[0,1]$$ denotes the interval of real numbers from $$0$$ to $$1$$ inclusive.

Given an input threshold $$t\in [0,1]$$, I need an algorithm which returns all maximum sized connected sub-graphs $$H\subseteq G$$, such that every node $$u\in H$$ has $$f(u)>t$$.

Can you please provide an algorithm suggestion or point me in the right direction?

• I think there is something I didn't get, because what prevents you from deleting all nodes with value under the threshold, then searching for the largest connected component? May 19 at 19:01
• – D.W.
May 20 at 2:37