Decycling bipartite graphs - Hertz, Alain (Journal of Graph Algorithms and Applications, 2021)
Let $G=(V,E)$ be a graph and let $S\subseteq V$ be a subset of its vertices. If the subgraph of $G$ induced by $V\setminus S$ is acyclic, then $S$ is said to be a decycling set of $G$. The size of a smallest decycling set of $G$ is called the decycling number of $G$. Determining the decycling number of a graph $G$ is NP-hard, even if $G$ is bipartite. We describe a tabu search procedure that generates decycling sets of small size for arbitrary bipartite graphs. Tests on challenging families of graphs show that the proposed algorithm improves many best-known solutions, thus closing or narrowing the gap to the best-known lower bounds.