Dukes, Peter J.Bowditch, Flora Caroline2021-03-012021-03-0120202020Bowditch, F. C. & Dukes, P. J. (2020). Local balance in graph decompositions. arXiv. https://arxiv.org/pdf/2002.08895.pdfhttps://arxiv.org/pdf/2002.08895.pdfhttp://hdl.handle.net/1828/12745In a balanced graph decomposition, every vertex of the host graph appears in the same number of blocks. We propose the use of colored loops as a framework for unifying various other types of local balance conditions in graph decompositions. In the basic case where a single graph with colored loops is used as a block, an existence theory for such decompositions follows as a straightforward generalization of previous work on balanced graph decompositions.enPreprint