On the Parameterized Complexity Of Grid Contraction
For a family of graphs π’, the π’-Contraction problem takes as an input a graph G and an integer k, and the goal is to decide if there exists F β E(G) of size at most k such that G/F belongs to π’. Here, G/F is the graph obtained from G by contracting all the edges in F. In this article, we initiate the study of Grid Contraction from the parameterized complexity point of view. We present a fixed parameter tractable algorithm, running in time c^k Β· |V(G)|^πͺ(1), for this problem. We complement this result by proving that unless fails, there is no algorithm for Grid Contraction with running time c^o(k)Β· |V(G)|^πͺ(1). We also present a polynomial kernel for this problem.
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