Algorithmic aspects of disjunctive domination in graphs

For a graph $G=(V,E)$, a set $D\subseteq V$ is called a \emph{disjunctive dominating set} of $G$ if for every vertex $v\in V\setminus D$, $v$ is either adjacent to a vertex of $D$ or has at least two vertices in $D$ at distance $2$ from it. The cardinality of a minimum disjunctive dominating set of $G$ is called the \emph{disjunctive domination number} of graph $G$, and is denoted by $\gamma_{2}^{d}(G)$. The \textsc{Minimum Disjunctive Domination Problem} (MDDP) is to find a disjunctive dominating set of cardinality $\gamma_{2}^{d}(G)$. Given a positive integer $k$ and a graph $G$, the \textsc{Disjunctive Domination Decision Problem} (DDDP) is to decide whether $G$ has a disjunctive dominating set of cardinality at most $k$. In this article, we first propose a linear time algorithm for MDDP in proper interval graphs. Next we tighten the NP-completeness of DDDP by showing that it remains NP-complete even in chordal graphs. We also propose a $(\ln(\Delta^{2}+\Delta+2)+1)$-approximation algorithm for MDDP in general graphs and prove that MDDP can not be approximated within $(1-\epsilon) \ln(|V|)$ for any $\epsilon>0$ unless NP $\subseteq$ DTIME$(|V|^{O(\log \log |V|)})$. Finally, we show that MDDP is APX-complete for bipartite graphs with maximum degree $3$

Independent transversal total domination versus total domination in trees

A subset of vertices in a graph G is a total dominating set if every vertex in G is adjacent to at least one vertex in this subset. The total domination number of G is the minimum cardinality of any total dominating set in G and is denoted by gamma(t)(G). A total dominating set of G having nonempty intersection with all the independent sets of maximum cardinality in G is an independent transversal total dominating set. The minimum cardinality of any independent transversal total dominating set is denoted by gamma(u) (G). Based on the fact that for any tree T, gamma(t) (T) <= gamma(u) (T) <= gamma(t) (T) + 1, in this work we give several relationship(s) between gamma(u) (T) and gamma(t) (T) for trees T which are leading to classify the trees which are satisfying the equality in these bound

Semi-Peripheral Realism: Nation and Form on the Borders of Europe

Despite its crucial function within the global capitalist system, the semi-periphery has received relatively little critical attention within the burgeoning field of world literature. As a transitional space between the core and the periphery, the semi-periphery is particularly sensitive to the economic, social and cultural uneveness of the world-system, making it invaluable for understanding the transformations and crises of capitalism. This thesis therefore explores the form and aesthetics of semi-peripheral literature by comparing a selection of novels from the borders of Europe. The study is structured around two case studies, both located on Europe’s continental fringes: the North Atlantic island nations, Iceland and the Faroe Islands, and Turkey; a set of very different social and cultural landscapes, which each illustrate a different historical transition to semi-peripherality. Starting in the North Atlantic, the first part of the thesis will explore the form and structures of colonial domination in Iceland and the Faroe Islands, and will consider how the systematic underdevelopment of both nations has impacted the peripheral nationalist aesthetics in the works of Halldór Laxness and William Heinesen. Expanding the project’s comparative scope to Turkey, the second part considers how the history of imperial decline and nation-building in the twentieth century are reflected in Orhan Pamuk and Latife Tekin’s semi-peripheral city- and borderscapes. Together the two sections cover different, but overlapping aspects of semi-peripherality, including the overdetermination of historical consciousness; the thematisation of language and translation; and the dialectical tension between ‘local’ and ‘global’ perspectives, which in different ways shape the particular aesthetics of semi-peripheral literature. Through comparative analysis of how each text mediates the distinct political, economic, cultural and social relations of the semi-periphery, this thesis argues that the conflicts and contradictions of the capitalist system are registered with particular intensity in the spaces that make up the semi-periphery, resulting in an antinomic literary aesthetic which testifies both to the unevenness of the capitalist world-system and to the radical potential of the semi-periphery as a space for political and social transformation. This project thereby engages in current debates about the intersections of postcolonial, comparative and world-literature and contributes to mapping literary registrations of the capitalist world-system

Distances and Domination in Graphs

This book presents a compendium of the 10 articles published in the recent Special Issue “Distance and Domination in Graphs”. The works appearing herein deal with several topics on graph theory that relate to the metric and dominating properties of graphs. The topics of the gathered publications deal with some new open lines of investigations that cover not only graphs, but also digraphs. Different variations in dominating sets or resolving sets are appearing, and a review on some networks’ curvatures is also present

Maximalism as a Cosmopolitan strategy in the art of Ruth Novaczek and Doug Fishbone

Ruth Novaczek and Doug Fishbone: Cosmpolitanism, Jewishness and Art This paper looks at the work of the experimental film-maker Ruth Novaczek and the artist Doug Fishbone to think through the relationship between the cosmopolitan imagination, Jewishness and the visual arts. I suggest through my analysis of their art work that both artists proffer a cosmopolitan subject that arises out of their Jewish subjectivity. I will do this in different ways, discussing the art- works both in their various forms as well as the subject matter within the films. I will think through two recent publications on the cosmopolitan and art by Marsha Merskimmon and Nikos Papastergiadis to discuss what is at stake in the cosmopolitan in relation to the two artist case studies. Central to my argument is a maximalist tendency that goes against the usual current paradigmatic trend of the “long look” that was first articulated by the influential André Bazin as more real than the dialectical editing techniques argued (and performed) by Sergei Eisenstein. But neither am I arguing for a return to Eisenstein. Maximalism, as offered by the work of these artists signifies an excessive overloading that allows the viewer to insert themselves into the narrative of the work through the editing, the collage, and in the density of the range of the material. Finally, I will be bringing the formal discussion into dialogue with the explicit meaning developed by the art-work. Each of these artists proffer an unstable subject that is profoundly formed out of their Jewish and Diasporic subjectivity. This arises not just out of the formal structural scaffolding of the work but in terms of the subject matter within the work. They both explicitly use Jewish cultural references as a normative navigational tools in the work and as a way of forming their cultural worlds. These references range from dialogues of Jewish characters in cinema, to Jewish jokes and use of Yiddish or Hebrew. Importantly Jewish religion or ritual is absent. For both of these artists the Holocaust is a backdrop but not as way to valorize a victim status but as a way to reach out to a wider humanity and to understand its legacies. This is done through multi-positionality and the questioning of what a ‘home’ might be outside of an attachment to a nation state or a singular geographic location and embracing that estrangement. In sum, I will argue that the work offers a reiterative provisionality as a refusal to judge or to know the world; instead there is an attempt to incorporate its complexities and range into the vision of the work, challenging the viewer to identify what is at stake in the work and in the subject

Afterlives : transcendentals, universals, others

If, as Walter Benjamin believed, ‘historical understanding is to be viewed primarily as an afterlife of that which is to be understood’, what are the afterlives of the central concepts of modern European philosophy today? These essays reflect on the afterlives of three such concepts – ‘the transcendental’, ‘the universal’ and ‘otherness’ – as they continue to animate philosophical discussion at and beyond the limits of the discipline. Anthropology, law, mathematics and politics each provide occasions for testing the historical durability and transformative capacity of these concepts. Contributors: Étienne Balibar, Antonia Birnbaum, Howard Caygill, Francis Cooper, Matt Hare, Marie Louise Krogh, Catherine Malabou