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...

We present observations and deliberations of one such project, the DSSG 2017 ‘Equitable Futures’ project, which investigates the ongoing gentrification process and the increasingly inequitable access to opportunities in Seattle. Similar processes can be observed in many major cities. The project connects issues usually analyzed in the disciplines of the built environment, geography, sociology, ...

INTRODUCTION Power imbalances within sexual relationships have significant implications for HIV prevention in sub-Saharan Africa. Little is known about how power influences the quality of a relationship, which could be an important pathway leading to healthy behavior around HIV/AIDS. METHODS This paper uses data from 448 heterosexual couples (896 individuals) in rural KwaZulu-Natal, South Afr...

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.

An equitable colouring of a balanced G-design (X,B) is a map φ∶B → C such that ∣bi(x) − bj(x)∣ ≤ 1 for any x ∈ X and i, j, with i ≠ j, being bi(x) the number of blocks containing the vertex x and coloured with the colour i. A c-colouring is a colouring in which exactly c colours are used. A c-colouring of type s is a colourings in which, for every vertex x, all the blocks containing x are colou...