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Many fixed-parameter tractable algorithms using a bounded search tree havebeen repeatedly improved, often by describing a larger number of branchingrules involving an increasingly complex case analysis. We introduce a novel andgeneral search strategy that branches on the forbidden subgraphs of a graphclass relaxation. By using the class of $P_4$-sparse graphs as the relaxedgraph class, we obtain efficient bounded search tree algorithms for severalparameterized deletion problems. We give the first non-trivial bounded searchtree algorithms for the cograph edge-deletion problem and the trivially perfectedge-deletion problems. For the cograph vertex deletion problem, a refinedanalysis of the runtime of our simple bounded search algorithm gives a fasterexponential factor than those algorithms designed with the help of complicatedcase distinctions and non-trivial running time analysis [21] and computer-aidedbranching rules [11].

Bounded Search Tree Algorithms for Parameterized Cograph Deletion: Efficient Branching Rules by Exploiting Structures of Special Graph Classes