Graph Square Roots of Small Distance from Degree One Graphs

Given a graph class ${\mathscr{H}}$ , the task of -Square Root problem is to decide whether an input G has square root H from . We are interested in parameterized complexity for classes that composed by graphs at vertex deletion distance most k maximum degree one, is, we looking such there modulator S size − disjoint union isolated vertices and edges. show different variants problems with constraints on number edges FPT when demonstrating algorithms running time $2^{2^{\mathcal {O}(k)}}\cdot n^{5}$ further our asymptotically optimal it unlikely double-exponential dependence could be avoided. In particular, prove VC-kRoot problem, asks cover k, cannot solved $2^{2^{o(k)}}\cdot n^{\mathcal {O}(1)}$ unless Exponential Time Hypothesis fails. Moreover, point out does not admit subexponential kernel P = NP.