Some equitably 3-colourable cycle decompositions

Let G be a graph in which each vertex has been coloured using one of k colours, say c(1), c(2),..., c(k). If an m-cycle C in G has n(i) vertices coloured c(i), i = 1, 2,..., k, and (i) - n(j) less than or equal to 1 for any i, j is an element of {1, 2,..., k}, then C is equitably k-coloured. An m-cycle decomposition C of a graph G is equitably k-colourable if the vertices of G can be coloured so that every m-cycle in C is equitably k-coloured. For m = 4,5 and 6, we completely settle the existence problem for equitably 3-colourable m-cycle decompositions of complete graphs and complete graphs with the edges of a 1-factor removed. (C) 2004 Elsevier B.V. All rights reserved.

Rehabilitating the common intention trust

Position of the common intention principle in Australia - the principle should continue to exist - evidentiary difficulties means that the principle is infrequently invoked - claimants who cannot produce sufficient evidence of a common intention may be entitled to relief via equitable estoppel or the joint endeavour principle - the doctrinal foundation of the common intention trust - alternative rationales for the common intention trust.

Burden of disease and injury in Aboriginal and non-Aboriginal populations in the Northern Territory

Objective: To quantify the burden of disease and injury for the Aboriginal and non-Aboriginal populations in the Northern Territory. Design and setting: Analysis of Northern Territory data for 1 January 1994 to 30 December 1998 from multiple sources. Main outcome measures: Disability-adjusted life-years (DALYs), by age, sex, cause and Aboriginality. Results: Cardiovascular disease was the leading contributor (14.9%) to the total burden of disease and injury in the NT, followed by mental disorders (14.5%) and malignant neoplasms (11.2%). There was also a substantial contribution from unintentional injury (10.4%) and intentional injury (4.9%). Overall, the NT Aboriginal population had a rate of burden of disease 2.5 times higher than the non-Aboriginal population; in the 35-54-year age group their DALY rate was 4.1 times higher. The leading causes of disease burden were cardiovascular disease for both Aboriginal men (19.1%) and women (15.7%) and mental disorders for both non-Aboriginal men (16.7%) and women (22.3%). Conclusions: A comprehensive assessment of fatal and non-fatal conditions is important in describing differentials in health status of the NT population. Our study provides comparative data to identify health priorities and facilitate a more equitable distribution of health funding.

Some equitably 3-colourable cycle decompositions of complete equipartite graphs

Let G be a graph in which each vertex has been coloured using one of k colours, say c(1), c(2),.. , c(k). If an m-cycle C in G has n(i) vertices coloured c(i), i = 1, 2,..., k, and vertical bar n(i) - n(j)vertical bar <= 1 for any i, j is an element of {1, 2,..., k}, then C is said to be equitably k-coloured. An m-cycle decomposition C of a graph G is equitably k-colourable if the vertices of G can be coloured so that every m-cycle in W is equitably k-coloured. For m = 3, 4 and 5 we completely settle the existence question for equitably 3-colourable m-cycle decompositions of complete equipartite graphs. (c) 2005 Elsevier B.V. All rights reserved.

The Politics of Decentralizing National Parks Management in the Philippines

International donors and state bureaucrats in the developing world have promoted decentralization reform as the primary means to achieve equitable, efficient and sustainable natural resource management. Relatively few studies, however, consider the power interests at stake. Why do state agencies decentralize power, what political patterns unfold, and how do outcomes affect the responses of resource users? This paper explores decentralization reform by investigating the political processes behind the Philippine state's decisions to transfer authority over national parks management to local government units. Drawing on a case of devolved management at Puerto Princesa Subterranean River National Park, Palawan Island, we examine how political motives situated at different institutional scales affect the broader process of decentralization, the structure of management institutions, and overall livelihood security. We demonstrate how power struggles between the Philippine state and City Government of Palawan over the right to manage the national park have impacted the livelihood support offered by community-based conservation. We conclude that decentralization may offer empowering resu

Socio-demographic variations in walking for transport and for recreation or exercise among adult Australians

Background: Walking is integral to strategies to promote physical activity. We identified socio-demographic variations in walking for transport, and for recreation or exercise. Methods: Representative population data (n = 3392) from Australia were collected using computer assisted telephone interviewing, to examine adults’ participation in moderate- or brisk-paced walking for transport and walking for recreation or exercise; walking “sufficient” to meet the current public health guideline (> 150 min/wk); and, the contributions of total walking to meeting the guideline for total physical activity. Results: Rates of sufficient walking for transport (10% for men, 9% for women) were lower than those for walking for recreation or exercise (14% for both genders). Few socio-demographic differences emerged. Men over age 60 y were significantly less likely (OR = 0.40) to walk for transport; men age 45 to 59 y were more likely (OR = 1.56) to walk for recreation or exercise. Walking contributed more toward meeting the current public health guideline among women (15% to 21%) than among men (6% to 8%). Conclusions: There is potential for socially equitable increases in participation, through a focus on both walking for transport and on walking for recreation or exercise; attention to gender differences would be helpful.