4 problems

Let $k$ be a positive integer and let $G$ be a graph of order $n$. For an independent set of order $k+1$, define … when $\alpha(G)\geq k+1$, and set $\sigma_{k+1}(G)=\infty$ otherw…

Let $D$ be a strong digraph with $n$ vertices. A pair is dominated or dominating when it is a pair of dominated or dominating nonadjacent vertices of $D$ as specified in the source…

Let $G$ be a graph, and consider a degree-sum condition for vertex pairs in a Hamiltonicity theorem. Degree-sum reduction conjecture. The lower bound in that degree-sum condition c…

Let $G$ be a graph of order $n$, let $k\geq 3$ be an integer, and let $n_{1},\dots,n_{k}$ be positive integers satisfying … Write $\sigma_2(G)$ for the minimum degree sum of two no…