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This PhD thesis is comprised of 3 results in computational geometry and graph theory. In the first paper, I demonstrate that the piercing number of a set S of pairwise intersecting convex shapes in the plane is bounded by O(\alpha(S)), where \alpha(S) is the fatness of the set S, improving upon the previous upper-bound of O(\alpha(S)^2). In the second article, I show that anagram-free vertex colouring of a 2\times n square grid requires a number of colours that increases with n. This answers an open question in Wilson's thesis and shows that even graphs of pathwidth 2 do not have anagram-free colouring with a bounded number of colours. The third article is a study on the geodesic anagram-free chromatic number of chordal and interval graphs. \emph{Geodesic anagram-free chromatic number} is defined as the minimum number of colours required to colour a graph such that all shortest paths between any pair of vertices are coloured anagram-free. In particular, I prove that the geodesic anagram-free chromatic number of a chordal graph G is 32p'w, where p' is the pathwidth of the subtree intersection representation graph (tree) of G, and w is the clique number of G. Additionally, I prove that the geodesic anagram-free chromatic number of an interval graph is bounded by 32p, where p is the pathwidth of the interval graph. This PhD thesis is comprised of 3 results in computational geometry and graph theory.

Thesis (MA)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: In one of Uganda’s main national newspapers, the New Vision, women and men advertise that they seek ‘white’ partners. Using emergent design, this study set out to explore this yearning for local - ‘white’ relationships. I conducted exploratory and semi-structured interviews with 20 of these women and men. As I started conducting the interviews, it became clear that this was a topic which provoked emotionally charged responses and a great deal of ‘identity work’, with participants identifying with, or disidentifying from, particular groups and categories, notably ‘prostitutes’ and ‘traditional’, ‘cultural’ or ‘modern’ women and men. Engaging critically with post-colonial writings and contemporary feminist research, I argue that my respondents provided important insights into the broader dynamics of gender, sexuality, race and power, as well as processes of identity construction in post-colonial Uganda. I explore the fantasy constructions and stereotypes perpetuating beliefs in ‘white’ superiority and address the various influences upon which respondents draw to bolster constructions of ‘whites’ as superior. These are marked by explicit beliefs in racial hierarchy, as well as ‘modernisation’ and ‘developmental’ discourses which positively associate ‘modernisation’ with ‘Westernisation.’ I discuss respondents’ negative constructions of local, ‘black’ men and women born out of past experiences with local partners. Male respondents expressed frustration with Ugandan women, whom they constructed as ‘money minded’, whom they believe forfeit dignity, for love of money, in their search for modernity. ‘Tradition’ and ‘culture’ were often invoked by men against women, who were seen as failing to live up to presumed cultural standards of femininity. I also explore female respondents’ appeals to ‘tradition’ and ‘culture’ which they feel benefit Ugandan men to the detriment of women and romantic relationships. I show that female respondents draw on discourses of Western ‘modernity’ and human rights, to illustrate the extent of gendered inequalities in Uganda, and find that Western humanism, embodied in the ‘white’ male, is constructed as a solution to their relationship dilemmas. / AFRIKAANSE OPSOMMING: In New Vision, een van Uganda se vernaamste nasionale nuusblaaie, plaas vroue, sowel as mans, advertensies waarin hulle aandui dat hulle op soek is na ‘wit’ metgeselle. Hierdie etnografiese studie steek voelers uit en probeer vasstel wat die motivering is om in verhoudings met ‘wit’ metgeselle betrokke te raak. Semigestruktuele onderhoude was met respondente (wat advertensies geplaas het) gevoer. Die studie vind dat respondente hul geslags- sowel as rasse-identiteit konstrueer. In sommige gevalle word dit gedoen deur identiteite te konstrueer waarmee hulle hulself nie wil assosieer nie. Deur bogenoemde in diepte te ondersoek, kry ons insig in die wyse waarop, in die kontemporêre Ugandese konteks, identiteitsvorming plaasvind. Ek ondersoek ook respondente se verbeeldingryke konstruksies en stereotipes wat die opvatting wil vestig dat ‘wit’ gelyk aan ‘superieur’ is. Ek spreek dan ook die verskeie beïnvloedingsvelde aan wat respondente gebruik en waarop hulle hul ‘wit is superieur’ opvatting bou. Ek dui aan dat die beïnvloedingsvelde dikwels gekenmerk word deur ‘n eksplisiete geloof in die bestaan van ‘n bepaalde hiërargie van ras. Diskoerse oor modernisering en ontwikkeling waarin ‘modernisering’ en ‘vooruitgang’ sterk geassosieer of gelykgestel word met verwestering is ook aan die orde van die dag. Voorts bespreek ek respondente se negatiewe konstruksie van plaaslike mans en vroue en die feit dat dit dikwels gebore is uit hul vorige (negatiewe) blootstelling aan plaaslike metgeselle. Manlike respondente spreek dikwels hul frustrasie uit met ‘geldgierige’ Ugandese vroue wat, volgens hulle, van hul eertydse waardigheid afstand doen in hul koorsagtige soek na modernisasie. Mans assosieer sterk met eie ‘tradisie’ en ‘kultuur’ en hulle voel dikwels dat vroue nie voldoen aan die mans se selfopgelegde kulturele standaarde van vroulikheid nie. Voorts ondersoek ek die pleidooie van vroue waarin hulle aanvoer dat sekere ‘tradisionele’ en ‘kulturele’ gebruike Ugandese mans onbillik bevoordeel. Ek dui aan dat vroulike respondente gebruik maak van redenasies oor Westerse modernisasie asook menseregte, in hul pogings om die mate van geslagsongelykheid wat in Uganda bestaan, uit te lig. Laastens vind ek dat Ugandese vroue Westerse humanisme (wat verpersoonlik word deur ‘wit’ mans) beskou as die oplossing vir hul verhoudingsprobleme.

Many Canadian children from minority status groups experience long-term academic complexities, influencing their sense of school belonging and engagement (Willms, 2003; Willms & Flanagan, 2007). Research demonstrates children with intersecting differences of race, ethnicity, language, and disability, and those in their middle years (10-13 years old), undergo heightened academic challenges (Blanchett, Klingner, & Harry, 2009; Cobbold, 2005). Within Toronto, one of the most diverse Canadian cities, this study explores the narratives of 6 middle years children with intersecting differences of race, ethnicity, language, and disabilities. The narratives highlight participants’ understandings of differences, learning, and inclusion. Specifically, what are marginalized children’s personal schooling experiences, and how may these insights support inclusive learning, teaching, and sense of belonging? Underpinned by conceptual lenses of (a) critical theory, from which stems critical pedagogy and critical multicultural education, and (b) the “new sociology of childhood” (Greene & Hogan, 2005), which includes social constructivist and participatory frames, this study employed qualitative narrative and critical discourse analysis research methods throughout 7 research sessions over a 4 month period. Accessing children’s multiple views, data collection included a “mosaic” (Clark & Moss, 2001) multi-method approach, such as semi-structured interviews with open-ended questions, writing activities, imaginative story games, photography, and drawings. The children’s narratives are re-presented as portrait narrative summaries within this paper. Surfacing findings include two predominant themes: (a) Participants’ conceptualizations of differences, race, ethnicity, language, culture, disability, and autism. Participants’ views relate to theories of denying differences, colour blindness, White discourse, and Othering; and (b) Interconnecting factors of inclusive and exclusive elements contributing to participants’ overall sense of school belonging. Additionally this theme highlights matters of meritocracy, individualization, and the “good” student. Underscoring both themes are notions of normalcy, and deficit and deficient-based discourses. Inviting student voice into educational conversations and research processes, this study demonstrates the importance of listening to voices of children with intersecting differences, as they may adeptly advance areas of inclusion and diversity.

Many Canadian children from minority status groups experience long-term academic complexities, influencing their sense of school belonging and engagement (Willms, 2003; Willms & Flanagan, 2007). Research demonstrates children with intersecting differences of race, ethnicity, language, and disability, and those in their middle years (10-13 years old), undergo heightened academic challenges (Blanchett, Klingner, & Harry, 2009; Cobbold, 2005). Within Toronto, one of the most diverse Canadian cities, this study explores the narratives of 6 middle years children with intersecting differences of race, ethnicity, language, and disabilities. The narratives highlight participants’ understandings of differences, learning, and inclusion. Specifically, what are marginalized children’s personal schooling experiences, and how may these insights support inclusive learning, teaching, and sense of belonging? Underpinned by conceptual lenses of (a) critical theory, from which stems critical pedagogy and critical multicultural education, and (b) the “new sociology of childhood” (Greene & Hogan, 2005), which includes social constructivist and participatory frames, this study employed qualitative narrative and critical discourse analysis research methods throughout 7 research sessions over a 4 month period. Accessing children’s multiple views, data collection included a “mosaic” (Clark & Moss, 2001) multi-method approach, such as semi-structured interviews with open-ended questions, writing activities, imaginative story games, photography, and drawings. The children’s narratives are re-presented as portrait narrative summaries within this paper. Surfacing findings include two predominant themes: (a) Participants’ conceptualizations of differences, race, ethnicity, language, culture, disability, and autism. Participants’ views relate to theories of denying differences, colour blindness, White discourse, and Othering; and (b) Interconnecting factors of inclusive and exclusive elements contributing to participants’ overall sense of school belonging. Additionally this theme highlights matters of meritocracy, individualization, and the “good” student. Underscoring both themes are notions of normalcy, and deficit and deficient-based discourses. Inviting student voice into educational conversations and research processes, this study demonstrates the importance of listening to voices of children with intersecting differences, as they may adeptly advance areas of inclusion and diversity.

This is a case study of the alternative labour union organization Central de Trabajadores de la Argentina (CTA) in Argentina and the most recent project under process striving for system change, named the Constituyente Social. The case under study is used to illustrate the perception of power in relation to aspirations for societal change among the left in Latin America. The overall struggle of the CTA and the Constituyente Social is to create a more just society based on a deepening of democracy, more participatory in character. Two understandings of power are presented, on the one hand is the taking power concept, inherited from the political struggles where the belief is that power needs to be taken from the elite in order to succeed with structural change in society. On the other hand is the creating power perception, best exemplified with the Zapatista movement in Mexico. There is no conquering of power in this view, but a creation and strengthening of power among the masses. The theoretical chapter presents a view that unites these two perceptions, arguing for the need to intersect the vertical (power taking) and the horizontal (power creating) struggles. The Constituyente Social is analyzed in relation to this intersection, providing concrete examples of where the two power perceptions are utilized, sometimes simultaneously. The overall conclusion is that the dichotomization usually done between the two understandings of power is incomplete and may even damage the struggle for societal change.