Waiter-Client clique-factor game

Fix two integers n,k, with n divisible by k, and consider the following game played players, Waiter Client, on edges of Kn. Starting all marked as unclaimed, in each round, picks yet unclaimed edges. Client then chooses one these to be added Client's graph, while other edge is Waiter's graph. wins if she eventually forces create a Kk-factor If does not manage do that, wins. For fixed k large enough n, it can easily shown that plays optimally (in particular, this an immediate consequence our result for such win quite fast). The question posed Clemens et al. how long will last aims fast can, tries delay her much he they both play optimally. We denote optimal number rounds τWC(Fn,Kk−fac,1). In present paper, we obtain first non-trivial lower bound quantity k. Together simple upper strategy al., gives2k/3−o(k)n≤τWC(Fn,Kk−fac,1)≤2knk+C(k), where C(k) constant dependent only o(k) term independent well.