Some equitably 3-colourable cycle decompositions

Adams, P, Bryant, D, Lefevre, J and Waterhouse, M (2004) Some equitably 3-colourable cycle decompositions. Discrete Mathematics, 284 1-3: 21-35. doi:10.1016/j.disc.2003.11.019

Author Adams, P
Bryant, D
Lefevre, J
Waterhouse, M
Title Some equitably 3-colourable cycle decompositions
Journal name Discrete Mathematics   Check publisher's open access policy
ISSN 0012-365X
Publication date 2004-01-01
Sub-type Article (original research)
DOI 10.1016/j.disc.2003.11.019
Volume 284
Issue 1-3
Start page 21
End page 35
Total pages 15
Editor P.L. Hammer
Place of publication Netherlands
Publisher Elsevier BV
Language eng
Subject C1
230101 Mathematical Logic, Set Theory, Lattices And Combinatorics
780101 Mathematical sciences
Abstract Let G be a graph in which each vertex has been coloured using one of k colours, say c(1), c(2),..., c(k). If an m-cycle C in G has n(i) vertices coloured c(i), i = 1, 2,..., k, and (i) - n(j) less than or equal to 1 for any i, j is an element of {1, 2,..., k}, then C is equitably k-coloured. An m-cycle decomposition C of a graph G is equitably k-colourable if the vertices of G can be coloured so that every m-cycle in C is equitably k-coloured. For m = 4,5 and 6, we completely settle the existence problem for equitably 3-colourable m-cycle decompositions of complete graphs and complete graphs with the edges of a 1-factor removed. (C) 2004 Elsevier B.V. All rights reserved.
Keyword Mathematics
Graph Colourings
Cycle Decompositions
Equitable Colourings
Steiner Triple
Q-Index Code C1

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Created: Wed, 15 Aug 2007, 13:04:53 EST