Hardness Results for Tournament Isomorphism and Automorphism.

A tournament is a graph in which each pair of distinct vertices is connected by exactly one directed edge. Tournaments are an important graph class, for which isomorphism testing seems to be easier to compute than for the isomorphism problem of general graphs. We show that tournament isomorphism and tournament automorphism is hard under DLOGTIME uniform AC0 many-one reductions for the complexity classes NL, C=L, PL (probabilistic logarithmic space), for logarithmic space modular counting classes ModkL with odd k ≥ 3 and for DET, the class of problems, NC1 reducible to the determinant. These lower bounds have been proven for graph isomorphism, see [21]. [ABSTRACT FROM AUTHOR]