Steiner trade spectra of complete partite graphs

The Steiner trade spectrum of a simple graph G is the set of all integers t for which there is a simple graph H whose edges can be partitioned into t copies of G in two entirely different ways. The Steiner trade spectra of complete partite graphs were determined in all but a few cases in a recent paper by Billington and Hoffman (Discrete Math. 250 (2002) 23). In this paper we resolve the remaining cases. (C) 2004 Elsevier B.V. All rights reserved.

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.

Packing lambda-fold complete multipartite graphs with 4-cycles

A maximum packing of any lambda-fold complete multipartite graph (where there are lambda edges between any two vertices in different parts) with edge-disjoint 4- cycles is obtained and the size of each minimum leave is given. Moreover, when lambda =2, maximum 4-cycle packings are found for all possible leaves.

A metacognitive contextual intervention to enhance error awareness and functional outcome following traumatic brain injury: A single-case experimental design

Very few empirically validated interventions for improving metacognitive skills (i.e., self-awareness and self-regulation) and functional outcomes have been reported. This single-case experimental study presents JM, a 36-year-old man with a very severe traumatic brain injury (TBI) who demonstrated long-term awareness deficits. Treatment at four years post-injury involved a metacognitive contextual intervention based on a conceptualization of neuro-cognitive, psychological, and socio-environmental factors contributing to his awareness deficits. The 16-week intervention targeted error awareness and self-correction in two real life settings: (a) cooking at home: and (b) volunteer work. Outcome measures included behavioral observation of error behavior and standardized awareness measures. Relative to baseline performance in the cooking setting, JM demonstrated a 44% reduction in error frequency and increased self-correction. Although no spontaneous generalization was evident in the volunteer work setting, specific training in this environment led to a 39% decrease in errors. JM later gained paid employment and received brief metacognitive training in his work environment. JM's global self-knowledge of deficits assessed by self-report was unchanged after the program. Overall, the study provides preliminary support for a metacognitive contextual approach to improve error awareness and functional Outcome in real life settings.

Adolescent tobacco-related associative memory: a cross-sectional and contextual analysis

Tobacco use is prevalent in adolescents, and understanding factors that contribute to its uptake and early development remains a critical public health priority. Implicit drug-related memory associations (DMAs) are predictive of drug use in older samples, but such models have little application to adolescent tobacco use. Moreover, extant research on memory associations yields little information on contextual factors that may be instrumental in the development of DMAs. The present study examined (a) the degree to which tobacco-related memory associations (TMAs) were associated with concurrent tobacco use and (b) the extent to which TMAs mediated the association of peer and self-use. A sample of 210 Australian high school students was recruited. Participants completed TMA tasks and behavioral checklists designed to obscure the tobacco-related focus of the study. Results showed that TMAs were associated with peer use, and TMAs predicted self-use. We found no evidence that TMAs mediated the association of peer and self-use. Future research might examine the emotive valence of implicit nodes and drinking behavior. The results have implications for testing the efficacy of consciousness-raising interventions for adolescents at risk of tobacco experimentation or regular use.

Decomposition of complete graphs into 5-cubes

Necessary conditions for the complete graph on n vertices to have a decomposition into 5-cubes are that 5 divides it - 1 and 80 divides it (it - 1)/2. These are known to be sufficient when n is odd. We prove them also sufficient for it even, thus completing the spectrum problem for the 5-cube and lending further weight to a long-standing conjecture of Kotzig. (c) 2005 Wiley Periodicals, Inc.

Some equitably 2-colourable cycle decompositions of multipartite 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 x(i) vertices coloured c(i), i = 1, 2,..., k, and vertical bar x(i) - x(j)vertical bar

On Hamilton cycle decomposition of 6-regular circulant graphs

The circulant graph Sn, where S ⊆ Zn \ {0}, has vertex set Zn and edge set {{x, x + s}|x ∈ Zn, s ∈ S}. It is shown that there is a Hamilton cycle decomposition of every 6-regular circulant graph Sn in which S has an element of order n.