On the computational complexity of upper fractional domination

The b-chromatic number of a graph

“…Many maximum and minimum graph parameters have 'minimum maximal' and 'maximum minimal' counterparts, respectively [9]. Much algorithmic activity has focused on such parameters relating to domination [4], independence [14,8] and irredundance [12]. However, the implicit partial order throughout is that of set inclusion.…”

A Dichotomy for Upper Domination in Monogenic Classes

“…The upper dominating set problem (i.e. the problem of finding an upper dominating set in a graph) is known to be NP-hard [2]. On the other hand, in some restricted graph families, the problem can be solved in polynomial time, which is the case for bipartite graphs [3], chordal graphs [8], generalized series-parallel graphs [7] and graphs of bounded clique-width [4].…”

On the Hardness of Approximating Some NP-optimization Problems Related to Minimum Linear Ordering Problem

“…The terminology of minimaximal and maximinimal is apparently first used by Peters et al [29], though the concept has received attention of many others, specially in connection with many graph problems. We may cite for example, minimum chromatic number and its maximum version, the achromatic number [9,12,20,21], maximum independent set and minimaximal independent set (minimum independent dominating set) [18,22,23,25], minimum vertex cover and maximinimal vertex cover [28,30], minimum dominating set and maximinimal dominating set [10,27], minimum vertex (edge) connectivity and maximinimal vertex (edge) connectivity [20,29] and a recent systematic study of minimaximal and maximinimal optimization problems by Manlove [30].…”