In the paper we consider the problems of equitable and semi-equitable coloring of vertices of cubic graphs. We show that in contrast to the equitable coloring, which is easy, the problem of semi-equitable coloring is NPcomplete within a broad spectrum of graph parameters. This affects the complexity of batch scheduling of unit-length jobs with cubic incompatibility graph on three uniform proces...

Need fulfillment has been found to be associated with numerous positive relationship outcomes, but its impact on stay-leave behavior is less clear. In the current study, we considered whether the fulfillment of different needs might differentially affect stay-leave behavior. We distinguished between needs that are personal in nature and those that are relational in nature. Central to our theore...

OBJECTIVES Quality of life and well-being in nursing homes are becoming more important in research and practice. Based on self-determination theory, the objective of this study is to examine the contribution of need fulfillment in the caring relationship to residents' subjective well-being. It was expected that the relation of need fulfillment in the caring relationship with well-being is media...

BACKGROUND Wearable activity trackers have become a viable business opportunity. Nevertheless, research has raised concerns over their potentially detrimental effects on wellbeing. For example, a recent study found that while counting steps with a pedometer increased steps taken throughout the day, at the same time it decreased the enjoyment people derived from walking. This poses a serious thr...

In this work we study the polytope associated with a 0/1 integer programming formulation for the Equitable Coloring Problem. We find several families of valid inequalities and derive sufficient conditions in order to be facet-defining inequalities. We also present computational evidence of the effectiveness of including these inequalities as cuts in a Branch & Cut algorithm.

In this paper, by the sorting method of vertices, it is obtained that the equitable chromatic number and the equitable chromatic threshold of the Cartesian products of fans with bipartite graphs.