4 problems

Let $G$ be a graph of order $n$, let $k$ be a positive integer, and let $c3_{k+1}(G)$ denote the minimum degree sum over every set of $k+1$ pairwise nonadjacent vertices of $G$. De…

Bondy's reverse degree-sum conjecture. If $\overline{p}\geq\Greekmath 0114 -1$, then

Let $H$ be a $3$-graph of order $n$, let $s$ be an integer with $2\le s\le n/3$, and let $H_{n,3,s}^2$ and $H_{n,3,s}^3$ be the two extremal $3$-graphs used in the degree-sum compa…

Let $G$ be a graph of sufficiently large order. For an integer $t\geq 1$, let $\sigma_t(G)$ denote the minimum degree sum over all sets of $t$ pairwise nonadjacent vertices of $G$.…