4 problems

Let $(d_1,\ldots,d_n)$ be a degree sequence with $n$ even, and let $h$ be the prescribed number of disjoint perfect matchings. A sequence realizes $h$ disjoint perfect matchings if…

Let $n\in\mathbb{N}$, let $d_1\ge d_2\ge\dots\ge d_n\ge1$ be integers, and let $h$ be a positive integer. The labelled h-factor is … where each tuple denotes the complete graph on…

A planar, 3-connected graph $G$ is strongly self-dual if it has a self-duality isomorphism $\tau:G\to G^*$ such that, for every pair of vertices $u,v$, $u\in\tau(v)$ if and only if…

Generalized realization conjecture. The conclusion of Theorem holds even for directed graphs $G$ that may contain $2$-cycles and $\Delta$-cliques.