$3.$H Another repurposing problem.

Let G $=($V$,$ E$)$ be an undirected graph with vertices V $=\{0,1,2,3,,$ n $1\},$ and edges defined by an array of adjacency

lists Adj$[0..$n $1].$ We say that an undirected graph F is h$-$resilient if every vertex in F has at least h neighbors.

Present an efficient algorithm that, given G and a target integer h $>0,$ finds the largest subgraph H in G that is h$-$resilient.

Hints: a beginner might try to start with the empty set, and insert vertices one$-$by$-$one. This cannot work.

A pro will start with G$,$ and remove vertices that cannot possibly belong to H$.$ This cannot be wrong $$ even if it eventually

throws away all of G$.$ But the question is: how do you do the bookkeeping needed to select bad vertices to throw way.

To keep things simple, just track the remaining vertices and any counts you need to identify what needs to be removed, and return

the vertex set that remains when the computation completes.