Book: Parameterized Algorithms by Marek Cygan (free to download legally)
Chapter about Multivariate polynomials on Page 353 (In the book not the pdf) Question 10.19:
Describe a Monte Carlo $2^{3k}n^{O(1)}$ - time polynomial-space algorithm for the Triangle Packing problem: given a graph $ G $ and a number $ k \in N $, decide whether $ G $ contains $ k $ disjoint triangles (subgraphs isomorphic to K3).
Hint 10.19 in Page 354: Use a similar approach as in the $2^{k}n^{O(1)}$ -time algorithm for $k$-path from this chapter (Page 333).
I tried to solve the problem using the hint, but without success unfortunately, there are solutions to the book? I would be happy to get help if it can be solved even without official solutions of the book but it is important to solve it using the hint they brought in order to use the tools learned in the same chapter.
Thanks in advance.