The Interchange Graphs of Tournaments with Minimum Score Vectors Are Exactly Hypercubes.

A Δ-interchange is a transformation which reverses the orientations of the arcs in a 3-cycle of a digraph. Let $${\fancyscript T}(S)$$ be the collection of tournaments that realize a given score vector S. An interchange graph of S, denoted by G( S), is an undirected graph whose vertices are the tournaments in $${\fancyscript T}(S)$$ and an edge joining tournaments $$T,T' \in {\fancyscript T}(S)$$ provided T′ can be obtained from T by a Δ-interchange. In this paper, we find a set of score vectors of tournaments for which the corresponding interchange graphs are hypercubes. [ABSTRACT FROM AUTHOR]