Some equitably 2-colourable cycle decompositions

Adams, P., Bryant, D. E. and Waterhouse, M. A. (2007) Some equitably 2-colourable cycle decompositions. Ars Combinatoria, 85 49-64.

Author Adams, P.
Bryant, D. E.
Waterhouse, M. A.
Title Some equitably 2-colourable cycle decompositions
Journal name Ars Combinatoria   Check publisher's open access policy
ISSN 0381-7032
Publication date 2007-01-01
Sub-type Article (original research)
Volume 85
Start page 49
End page 64
Total pages 16
Editor Vanstone, S. A.
Allson, J. L.
Alspach, B.
et al.
Place of publication Winnipeg, Canada
Publisher Charles Babbage Research Centre
Language eng
Subject 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 ni vertices coloured c(i), i = 1, 2,., k, and vertical bar n(i) - n(j)vertical bar <= 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-colourabte 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 2-colourable m-cycle decompositions of complete graphs and complete graphs with the edges of a I-factor removed.
Keyword Mathematics
Q-Index Code C1

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Created: Fri, 04 Apr 2008, 00:04:42 EST by Marie Grove on behalf of School of Mathematics & Physics