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On the complexity of H-colouring planar graphs
MacGillivray, G.,Siggers, M. North-Holland Pub. Co ; Elsevier Science Ltd 2009 Discrete mathematics Vol.309 No.18
We show that if H is an odd-cycle, or any non-bipartite graph of girth 5 and maximum degree at most 3, then planar H-COL is NP-complete.
Reconfiguring k-colourings of Complete Bipartite Graphs
Celaya, Marcel,Choo, Kelly,MacGillivray, Gary,Seyffarth, Karen Department of Mathematics 2016 Kyungpook mathematical journal Vol.56 No.3
Let H be a graph, and $k{\geq}{\chi}(H)$ an integer. We say that H has a cyclic Gray code of k-colourings if and only if it is possible to list all its k-colourings in such a way that consecutive colourings, including the last and the first, agree on all vertices of H except one. The Gray code number of H is the least integer $k_0(H)$ such that H has a cyclic Gray code of its k-colourings for all $k{\geq}k_0(H)$. For complete bipartite graphs, we prove that $k_0(K_{\ell},r)=3$ when both ${\ell}$ and r are odd, and $k_0(K_{\ell},r)=4$ otherwise.
The Internationalisation of Fashion Consumption. Challenges for the Twenty-first Century
Hann, M. A.,MacGillivray, M. S. The Costume Culture Association Department of Clot 2000 Fashion, industry and education Vol.3 No.3
The nature of internationalisation is explored and the historical stages in the process described. A series of profiles of fashion companies, which have pursued policies of internationalisation, is presented. The challenges faced by fashion producers and retailers, as they enter the twenty-first century, are identified and the changing context of fashion consumption if recognised.
COMPILE—A Generic Benchmark Case for Predictions of Marine Pile-Driving Noise
Lippert, Stephan,Nijhof, Marten,Lippert, Tristan,Wilkes, Daniel,Gavrilov, Alexander,Heitmann, Kristof,Ruhnau, Marcel,von Estorff, Otto,Schafke, Alexandra,Schafer, Ingo,Ehrlich, Jan,MacGillivray, Alexa IEEE 2016 IEEE JOURNAL OF OCEANIC ENGINEERING - Vol.41 No.4
<P>The prediction of underwater noise emissions from impact pile driving during near-shore and offshore construction activities and its potential effect on the marine environment has been a major field of research for several years. A number of different modeling approaches have been suggested recently to predict the radiated sound pressure at different distances and depths from a driven pile. As there are no closed-form analytical solutions for this complex class of problems and for a lack of publicly available measurement data, the need for a benchmark case arises to compare the different approaches. Such a benchmark case was set up by the Institute of Modelling and Computation, Hamburg University of Technology (Hamburg, Germany) and the Organisation for Applied Scientific Research (TNO, The Hague, The Netherlands). Research groups from all over the world, who are involved in modeling sound emissions from offshore pile driving, were invited to contribute to the first so-called COMPILE (a portmanteau combining computation, comparison, and pile) workshop in Hamburg in June 2014. In this paper, the benchmark case is presented, alongside an overview of the seven models and the associated results contributed by the research groups from six different countries. The modeling results from the workshop are discussed, exhibiting a remarkable consistency in the provided levels out to several tens of kilometers. Additionally, possible future benchmark case extensions are proposed.</P>