4 problems

A Hamilton decomposition of a graph is a decomposition of its edge-set into Hamilton cycles. Alspach's conjecture. Every abelian Cayley graph of even degree admits a decomposition…

Let $G$ be an $(n,d,lambda)$-graph, meaning a $d$-regular graph on $n$ vertices whose non-trivial adjacency-matrix eigenvalues have absolute value at most $lambda$. A Hamilton deco…

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.