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, Peter
Bryant, Darryn E.
Jordon, Heather
Title Edge-coloured cube decompositions
Journal name Aequationes Mathematicae   Check publisher's open access policy
ISSN 0001-9054
Publication date 2006-12
Sub-type Article (original research)
DOI 10.1007/s00010-006-2826-x
Volume 72
Issue 3
Start page 213
End page 224
Total pages 12
Editor Ludwig Reich
Detlef Gronau
Place of publication Switzerland
Publisher Birkhauser Verlag
Collection year 2006
Language eng
Subject C1
230101 Mathematical Logic, Set Theory, Lattices And Combinatorics
780101 Mathematical sciences
Abstract 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.
Q-Index Code C1

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Created: Wed, 15 Aug 2007, 10:18:03 EST