Tournament Fixing Parameterized by Feedback Vertex Set Number Is FPT

A knockout (or single-elimination) tournament is a format of competition that very popular in practice (particularly sports, elections and decision making), which has been extensively intensively studied from theoretical point view for more than decade. Particular attention devoted to the Tournament Fixing problem, where, roughly speaking, objective determine whether we can conduct way makes our favorite player win. Here, part input graph D encodes winner each possible match. sequence papers parameterized complexity with respect feedback arc set number (fas) Given this parameter yielded tractability, it asked explicitly repeatedly FPT also vertex (fvs) D. We answer question positively. In fact, although fvs be arbitrarily smaller fas, attain same dependency on time complexity. So, additionally, work subsumes best known algorithm as.