Skip Navigation

Journal of the London Mathematical Society 1988 s2-37(121):14-24; doi:10.1112/jlms/s2-37.121.14
© 1988 by London Mathematical Society
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Ellingham, M. N.
Right arrow Articles by Wormald, N. C.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The London Mathematical Society

Isomorphic Factorization of Regular Graphs and 3-Regular Multigraphs

M. N. Ellingham and N. C. Wormald

Department of Combinatorics, and Optimization, University of Waterloo Waterloo, Ontario N2L 3GI, Canada
Department of Mathematics, University of Auckland Private Bag, Auckland, New Zealand

Received 5 November 1984. Revision received 17 February 1987.

A multigraph G is divisible by t if its edge set can be partitioned into t subsets, such that the subgraphs (called factors) induced by the subsets are all isomorphic. If G has e(G) edges, then it is t-rational if it is divisible by t or if t does not divide e(G). A short proof is given that any graph G is t-rational for all t ≥ {xi}'(G) (the chromatic index of G), and thus any r-regular graph is t-rational for all t ≥ r+1. The main result of this paper is that all 3-regular multigraphs are divisible by 3, in such a way that the components of each factor are paths of length 1 or 2. It follows that 3-regular graphs are t-rational for all t ≥ 3. The proofs rely on edge-colouring techniques.

Current address: Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37235, USA


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.