4 problems

Let $n$ be sufficiently large, and let $G$ be a regular tripartite tournament on $3n$ vertices. Denote by ${\mathcal T}_\triangle$ the known regular tripartite tournament obtained…

A regular bipartite tournament is an orientation of the complete balanced bipartite graph $K_{2n,2n}$ in which every vertex has indegree and outdegree $n$. A Hamilton decomposition…

Generalised Alspach conjecture. If $G$ satisfies condition $P_i$, then $G$ has a decomposition into $i$ Hamiltonian double-rays and $k-i$ Hamiltonian circles. Here a Hamiltonian do…

Tripartite tournament conjecture. Every regular tripartite tournament has a Hamilton decomposition.