The UK has been identified as the standout construction market in Europe and is set to become Europe's largest construction market by 2030. However, UK construction productivity performance is regarded as weak with low skills levels considered to be a key contributory factor. Consequently, Offsite construction has been identified by UK Government as a vehicle for improving productivity levels if the skills deficiencies in this particular market segment can be addressed. A series of projects were therefore launched by the UK Commission for Employment and Skills (UKCES) to encourage an R&D approach to skills and development application in the workplace. This paper reports on one of these research projects, a University and Industry collaboration between two of the largest offsite timber platform frame manufacturers in the UK. The paper explains how a needs analysis process was utilised to develop skills training content tailored to the immediate needs of the industry partners. It also explores how working with academia and a wider community of stakeholders allowed this training content to result in sector level impact via knowledge exchange activities and generic skills material creation.Finally, the novel approach of utilising 'Hoshin' planning to form a larger regional Offsite HUB (Scotland) Community of Practice, with a developed plan for collaboration aligned with international offsite research objectives, is also explained. This is particularly relevant given the recent UK Farmer review "Modernise or Die -time to decide the industry future", the most recent in a series of calls from government and other respected sources for improved levels of productivity and cultural change in the construction sector.The case study presented in this paper is evidence of success in mobilising industry through creating communities of practice to advance the construction sector regionally.It also provides a generalisable method that is reproducible by other university-industry cohorts in order to realise shared industry wide goals.

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Abstract. Let G be a simple undirected graph on n vertices and let S(G) be the class of real symmetric n × n matrices whose nonzero off-diagonal entries correspond exactly to the edges of G.and a vertex v of G, the question is addressed of whether or not there exists A ∈ S(G) with eigenvalues λ 1 , . . . , λn such that A(v) has eigenvalues µ 1 , . . . , µ n−1 , where A(v) denotes the matrix with the vth row and column deleted. General results that apply to all connected graphs G are given first, followed by a complete answer to the question for Kn. Since the answer is constructive it can be implemented as an algorithm; a Mathematica code is provided to do so. Finally, for all connected graphs on 4 vertices it is shown that the answer is affirmative if all six inequalities are strict.