12 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…

Degree-sum path improvement. If

Reverse degree-sum improvement. If

Degree-sum improvement. If

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

Let $H$ be a 3-graph of order $n$, let $\sigma_2(H)$ be the minimum of $\deg(u)+\deg(v)$ over all adjacent vertices $u,v$, and let $H^2_{n,s}$ be the 3-graph whose vertex set is pa…

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 $G$.…

Let $G$ be a 3-edge-connected graph of order $n$, and let $\overline{\sigma}_2(G)$ denote the minimum relevant degree-sum parameter. Let $\mathcal{SL}$ denote the class represented…

Let $G$ be a graph, let $p$ denote its order, let $c$ denote the length of a longest cycle, let $\kappa$ denote the connectivity of $G$, and let $\sigma_r$ denote the minimum degre…

Let $G$ be a graph, let $p$ denote its order, let $c$ denote the length of a longest cycle, and let $\sigma_r$ denote the minimum degree sum of an independent set of $r$ vertices.…

Let $G$ be a graph, let $p$ denote its order, let $c$ denote the length of a longest cycle, let $\bar\kappa(G)$ denote its connectivity, and let $\sigma_r$ denote the minimum degre…

Let $G$ be a finite undirected graph with minimum degree $\delta$, and let $C$ be a longest cycle in $G$. Write $\overline{p}$ and $\overline{c}$ for the lengths of a longest path…