We study the algorithmic task of finding a large independent set in sparse Erdős– Rényi random graph with $n$ vertices and average degree $d$. The maximum is known to have size $(2 \log d / d)n$ double limit $n \to \infty$ followed by $d \infty$, but best polynomial-time algorithms can only find an half-optimal $(\log d)n$. show that class low-degree polynomial sets no larger, improving upon re...

Let $k$ be a fixed integer. We determine the complexity of finding a $p$-partition $(V_1, \dots, V_p)$ of the vertex set of a given digraph such that the maximum out-degree of each of the digraphs induced by $V_i$, ($1\leq i\leq p$) is at least $k$ smaller than the maximum out-degree of $D$. We show that this problem is polynomial-time solvable when $p\geq 2k$ and ${\cal NP}$-complete otherwise...

maslach and jackson first introduced the concept of ‘burnout’- a state of physical and emotional exhaus- tion emerging from work conditions- in 1980. the importance of investigations of burn out lies in the fact that it is directly related to the quality of teaching. there are three basic criteria set to predict, evaluate, and prevent burnout: depersonalization, emotional exhaustion, and person...

let $d$ be a digraph with vertex set $v(d)$. for vertex $vin v(d)$, the degree of $v$,denoted by $d(v)$, is defined as the minimum value if its out-degree and its in-degree.now let $d$ be a digraph with minimum degree $deltage 1$ and edge-connectivity$lambda$. if $alpha$ is real number, then the zeroth-order general randic index is definedby $sum_{xin v(d)}(d(x))^{alpha}$. a digraph is maximall...