5 problems

Let $K_{2n}$ be the complete graph on $2n$ vertices. A 1-factorization is a decomposition of its edges into perfect matchings, and it is perfect when the union of any two distinct…

Let $K_{4n+1}$ be a complete graph on $4n+1$ vertices, where … and both $m_1$ and $m_2$ are even. A graphical pair $((G,g),(H,h))$ without loops consists here of graphs $G$ and $H$…

Let $G$ be a regular graph of even order. The 1-factorization conjecture. Every regular graph of even order with sufficiently high degree is $1$-factorizable. Here, $1$-factorizabl…

Plantholt–Tipnis multigraph 1-factorization conjecture. If the degree of $G$ is at least $rn$, then $G$ is 1-factorizable.

Chetwynd–Hilton 1-factorization conjecture. Every regular simple graph of order $2n$ and degree at least $n$ is 1-factorizable.