Algorithm to compute maximum independent set of graph with maximum block size k with comlexity $O(f(k)\cdot p(|V(G)|)$

Question

Definitions

Definition block: Let $G$ be a undirected Graph. A maximal 2-connected subgraph (subgraph without biconnected component) of $G$ is called a block.

Definition maximum independent set: An independent set is a set of vertices in a graph, no two of which are adjacent. A maximum independent set is an independent set of largest possible size for a given graph $G$.

Question

Let $G$ be a undirected, connected Graph. All blocks $B\subseteq G$ satisfy $|V(B)| \leq k$. Let $f(k)$ be a be any function, and $p(|V(G)|)$ any polynomial. The task is, to find an Algorithm, that finds a maximum independent set of $G$ with $O(f(k)\cdot p(|V(G)|)$ complexity.

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So far i know how to compute all blocks in $O(|V(G)|^2\cdot |E(G)|)$ and maximum independent sets via brute force in $O(2^{|V(G)|}\cdot |V(G)|^2)$. My guess is, that i have to brute force independent sets of every block in the graph and then somehow merge the the right solutions/i-sets to one set. I struggle with the latter. Thanks in andvance for any answers/hints.

Answer 1

Solved the problem myself. As a hint to anyone who wants to find an algorithm: you have to calculate the block-graph (this is a german link, the english wiki for block-graph is something else) and then use the fact, that a block-graph always is a tree.