Usually questions deal with claw-free graphs, but suppose we are given a graph $G$ and there are $k$ vertex-disjoing claws in the graph, how can we derive a randomised algorithm using color coding to find them. My intuition is to approach this with $k$ colors, but not really sure how to start it. Could someone give me some hints and ideas on how to approach this?
Finding vertex-disjoint copies of a subgraph $H$ in a graph $G$ is known as Graph Packing.
You could use Divide and Color to find the claws in $O^*(4^k)$, also deterministically (look for Chen et al. construction of universal set for derandomization).