Square Root Finding In Graphs

Abstract: Root and root finding are concepts familiar to most branches of mathematics. In graph theory, H is a square root of G and G is the square of H if two vertices x,y have an edge in G if and only if x,y are of distance at most two in H. Graph square is a basic operation with a number of results about its properties in the literature. We study the characterization and recognition problems of graph powers. There are algorithmic and computational approaches to answer the decision problem of whether a given graph is a certain power of any graph. There are polynomial time algorithms to solve this problem for square of graphs with girth at least six while the NP-completeness is proven for square of graphs with girth at most four. The girth-parameterized problem of root fining has been open in the case of square of graphs with girth five. We settle the conjecture that recognition of square of graphs with girth 5 is NP-complete. This result is providing the complete dichotomy theorem for square root finding problem.

University Faculty Members’ Understanding of Their Role: Identity, Power, and Silence

This qualitative study was conducted to explore tenured faculty members’ understandings of their roles as professors. Tenure is an institutional means to enact academic freedom, which allows tenured faculty members to investigate topics of their choosing free from external influence. Academic freedom also enables faculty members to be public intellectuals who shape and critique social policies and make knowledge assertions. In effect, the faculty members are institutionally protected to speak truth to power. Purposeful sampling of 9 participants from 2 universities yielded 3 major themes: professorial identity (shaped by such factors as career stage, university culture, and faculty affiliation), professorial power (powers that participants experienced as well as the ways in which they exercised power), and professorial silencing (as a response to fiscal realities coupled with numerous governance issues). While participants were cognizant of the powers that affected their freedoms, they were less aware of the ways in which their position afforded them powers. Subtle but more potent forms of power were at play for tenured professors, but the participants saw themselves as having to work within institutional and financial constraints that limited their freedom to speak out on controversial issues. Faculty members were, thus, silenced and at times chose to self-silence. The context of the present-day university, governance models, and the financial issues affecting universities and departments worked in concert to silence this critical voice in society.

Letter to W.D. Woodruff from E.C. Wheeler Jr. of N.W. Harris and Co. Bankers of New York

Letter to W.D. Woodruff from E.C. Wheeler Jr. of N.W. Harris and Co. Bankers of New York (1 page, printed) saying that he is pleased that Mr. Woodruff has decided to take the $10,000 Dominion Powers at 90 and interest. They will expect Mr. Woodruff in a few days, Dec. 10, 1907.

Broadside with a coloured picture of a case engine and tender [steam engine]

Broadside, 47 cm. x 31 cm. with a coloured picture of a case engine and tender [steam engine] printed by Meyer-Rotier of Milwaukee. On the back is a sketch of a building. This has a stamp on the back which indicates that this is an exhibit in the High Court of Justice in Coburg in the case of Bigelow vs. Powers et al. This item has been torn down the middle and taped. This does not affect the text nor picture, Oct. 11, 1909.

The Supreme Court’s Understanding of Federalism: Efficiency at the Expense of Diversity

This paper is an examination of the Supreme Court of Canada's interpretation of federalism since constitutional repatriation in 1982. It argues that the lure of centralist efficiency is overpowering a fundamentally important part of our federal order: regionalism. The author contends that changes made by the Court to certain fundamental concepts of Canadian constitutional law now provide Parliament with greater latitude than before in the exercise of its legislative powers. According to the author, these changes are disturbing because they are structured so as to preclude consideration of the legitimate concerns of regional polities. Furthermore, he argues that the Court has reinforced the central government's power to regulate the economy, including intraprovincial matters affecting trade, by resorting to highly functional tests that emphasize economic efficiency over other criteria. This, he claims, makes it more difficult to invoke legitimate regional interests that would lead to duplication, overlapping and even, in the eyes of some, inefficiency. The author the focuses on the Court's treatment of environmental protection in an attempt to show the tension between the Court's desire to use a functional approach and the need to recognize regional interests. Finally, through an examination of recent case law, he attemps to demonstrate that the Court's dominant perspective remains functional despite its endorsement of a more community-oriented undestanding of federalism in Secession Reference. If the Court chooses to proceed in this manner, it will alienate regional polities and may encourage them to choose more radical means of asserting their differences. Further, the author argues that strict adherence to the functional effectiveness approach will undermine the very values that federalism is meant to promote.

L’interaction entre le droit privé fédéral et le droit civil québécois en matière d’effets de commerce: perspective constitutionnelle

Un résumé en anglais est également disponible.

El extranjero y el derecho a la justicia en Canadá tras el 11 de septiembre

After the events of September 11, the fear of terrorism led to the adoption of new anti-terrorist measures (elimination of appeals available to foreigners, reduction of legal aid, increased powers of detention, easier use of security certificates…). But in Canadian Charter of Rigths and Freedoms only the right to vote and be elected, the right to enter and remain in the country and the minority language educational rights specifically protect citizens. The protection of Canadian citizens cannot be based on the denial of foreigner´s rights. The same rights are at stake: The violation of a foreigners´s rights is a violation of citizen´s rights.

Defining the crime of aggression : cutting the Gordian knot ?

"Mémoire présenté à la Faculté des Études supérieures en vue de l'obtention du grade de LL.M. en Maîtrise en droit Option recherche"

La réglementation d'Internet dans le fédéralisme canadien : l'étendue des pouvoirs du parlement fédéral

"Mémoire présenté à la Faculté des études supérieures en vue de l'obtention du grade de maître en droit (LL.M)"

Les politiques et pratiques commerciales québécoises en matière de boissons alcooliques dans le contexte du droit commercial international

"Mémoire présenté à la Faculté des études supérieures en vue de l'obtention du grade de Maîtrise en Droit (LL.M.)"

Fédéralisme, concurrence intergouvernementale et intérêt national dans le domaine des valeurs mobilières au Canada

La structure de la réglementation des valeurs mobilières au Canada fait périodiquement l'objet d'un débat public et une des questions sous-jacentes est celle du partage des compétences législatives prévu par la Constitution canadienne. Le débat a été relancé en 2003 par la recommandation d'un comité de personnes averties de centraliser cette réglementation au fédéral. Les provinces, sauf l'Ontario, demeurent opposées à l'idée, préférant plutôt l'harmonisation réglementaire. Pour alléger le fardeau réglementaire des émetteurs, elles tentent également de mettre en oeuvre un « régime de passeport ». Ce débat présente la question comme un jeu à somme nulle, occultant ainsi certains principes fondamentaux du fédéralisme: innovation provinciale dans une union économique nationale. Dans ce mémoire, nous proposons donc une structure réglementaire, basée sur la théorie de la concurrence intergouvernementale, qui s'harmonise avec les compétences du gouvernement fédéral et des provinces tout en optimisant leurs atouts respectifs.

La compétence du tribunal arbitral dans l'arbitrage commercial

"Mémoire présenté à la Faculté des études supérieures En vue de l'obtention du grade de Maîtrise en droit (L.L.M)"

L'interprétation et le contrôle de la légalité des résolutions du Conseil de sécurité

"Mémoire présenté à la Faculté des études supérieures En vue de l'obtention du grade de Maître en droit (L.L.M)"

Les opérations scrutées sous l'angle de l'intérêt public par les organismes de réglementation des valeurs mobilières : entre efficience et duplicité

"Mémoire présenté à la Faculté des études supérieures en vue de l'obtention du grade de Maîtrise en droit (LL.M) option droit des affaires"