Spanning trees orthogonal to one-factorizations of \(K_{2n}\). (Q2715971)

The authors improve some results on the Hollingsworth-Brualdi conjecture which claims that for any one-factorization \(F\) of \(K_{2n}\) there exists a decomposition of \(K_{2n}\) into spanning trees orthogonal to \(F\). The authors construct three such trees for every \(K_{2n}\) (this result improves two such trees known before) and exhibit infinitely many complete graphs with an orthogonal decomposition into spanning trees with respect to the standard one-factorization \(GK_{2n}\).