Complementary cycles containing prescribed vertices in tournaments (Q1972131)

Let \(x\) and \(y\) be nodes of a tournament \(T\) with at least eight nodes such that \(T\) remains 2-connected after the arc joining \(x\) and \(y\) is removed. The authors show, among other things, that \(T\) has two node-disjoint cycles \(C_x\) and \(C_y\) containing nodes \(x\) and \(y\), respectively, such that every node of \(T\) belongs either to \(C_x\) or to \(C_y\).