Star-factors of tournaments

الأصل · EN

Let Sₘ denote the m-vertex simple digraph formed by m-1 edges with a common tail. Let f(m) denote the minimum n such that every n-vertex tournament has a spanning subgraph consisting of n/m disjoint copies of Sₘ. We prove that m lg m - m lg lg m <= f(m) <= 4m² - 6m for sufficiently large m.