# Edge-coloured cube decompositions

Adams, Peter, Bryant, Darryn E. and Jordon, Heather (2006) Edge-coloured cube decompositions. Aequationes Mathematicae, 72 3: 213-224. doi:10.1007/s00010-006-2826-x

Author Adams, PeterBryant, Darryn E.Jordon, Heather Edge-coloured cube decompositions Aequationes Mathematicae   Check publisher's open access policy 0001-9054 2006-12 Article (original research) 10.1007/s00010-006-2826-x 72 3 213 224 12 Ludwig ReichDetlef Gronau Switzerland Birkhauser Verlag 2006 eng C1230101 Mathematical Logic, Set Theory, Lattices And Combinatorics780101 Mathematical sciences An edge-colored graph is a graph H together with a function f:E(H) → C where C is a set of colors. Given an edge-colored graph H, the graph induced by the edges of color c C is denoted by H(c). Let G, H, and J be graphs and let μ be a positive integer. A (J, H, G, μ) edge-colored graph decomposition is a set S = {H 1,H 2,...,H t} of edge-colored graphs with color set C = {c 1, c 2,..., c k} such that Hi ≅ H for 1 ≤ i ≤ t; Hi (cj) ≅ G for 1 ≤ i ≤ t and ≤ j ≤ k; and for j = 1, 2,..., k, each edge of J occurs in exactly μ of the graphs H 1(c j ), H 2(c j ),..., H t (c j ). Let Q 3 denote the 3-dimensional cube. In this paper, we find necessary and sufficient conditions on n, μ and G for the existence of a (K n ,Q 3,G, μ) edge-colored graph decomposition. © Birkhäuser Verlag, Basel 2007. C1

 Document type: Journal Article Article (original research) Excellence in Research Australia (ERA) - Collection 2007 Higher Education Research Data Collection School of Physical Sciences Publications

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