NC algorithms for antidirected hamiltonian paths and cycles in tournaments

Abstract

Two classical theorems about tournaments state that a tournament with no less than eight vertices admits an antidirected Hamiltonian path and an even cardinality tournament with no less than sixteen vertices admits an antidirected Hamiltonian cycle. Sequential algorithms for finding such a path as well as a cycle follow directly from the proofs of the theorems. Unfortunately, these proofs are inherently sequential and can not be exploited in a parallel context. In this paper we propose new proofs leading to efficient parallel algorithms.