Paths in tournaments a simple proof of Rosenfeld's Conjecture

Abstract

Rosenfeld Conjectured in 1972 that there exists an integer K $\geq$ 8 such that any tournament of order n $\geq$ K contains any Hamiltonian oriented path. In 2000, Havet and Thomass\'e proved this conjecture for any tournament with exactly 3 exceptions. We give a simplified proof of this fact.