Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-05T06:54:44.035Z Has data issue: false hasContentIssue false
  • English
  • Français

Isomorphic factorization of regular graphs of even degree

Part of: Graph theory

Published online by Cambridge University Press:  09 April 2009

M. N Ellingham
M. N Ellingham
Affiliation:
Department of Combinatorics and OptimizationUniversity of WaterlooWaterloo, Ontario N2L 3G1, Canada
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A graph 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. Such an edge partition is an isomorphic factorization. It is proved that a 2k-regular graph with an even number of vertices is divisble by 2k provided it contains either no 3-cycles or no 5-cycles. It is also shown that any 4-regular graph with an even number of vertices is divisible by 4. In both cases the components of the factors found are paths of length 1 and 2, and the factorizations can be constructed in polynomial time.

MSC classification

Secondary: 05C70: Factorization, matching, partitioning, covering and packing
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 44 , Issue 3 , June 1988 , pp. 402 - 420
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Edmonds, J. and Johnson, E. L., ‘Matching, euler tours and the Chinese postman’, Math. Programming 5 (1973), 88–123.CrossRefGoogle Scholar
[2]Ellingham, M. N., ‘Isomorphic factorization of r-regular graphs into r parts’, to appear in Discrete Math. (Available as Research Report CORR 85–7, Dept. of Combinatorics and Optimization, University of Waterloo, 1985.)Google Scholar
[3]Ellingham, M. N. and Wormald, N. C., ‘Isomorphic factorization of regular graphs and 3-regular multigraphs’, J. London Math. Soc., to appear (Available as Research Report CORR 85–6, Dept. of Combinatorics and Optimization, University of Waterloo, 1985.)Google Scholar
[4]Fleischner, H., Eulerian graphs, Selected topics in graph theory 2, edited by Beineke, L. W. and Wilson, R. J., Chapter 2, Academic Press, London, 1983.)Google Scholar
[5]Hopcroft, J. E. and Karp, R. M., ‘An n5/2 algorithm for maximum matching in a bipartite graph’, SIAM J. Computing 2 (1973), 225–231.Google Scholar
[6]König, D., ‘Über Graphen und ihre Anwendung auf Determinantentheorie und Mengenlehre’, Math. Ann. 77 (1916), 453–465.Google Scholar
[7]Petersen, J., ‘Die Theorie der reguläen Graphen’, Acta Math. 15 (1891), 193–220.CrossRefGoogle Scholar
[8]Wormald, N. C., ‘Isomorphic factorizations VII. Regular graphs and tournaments’, J. Graph Theory 8 (1984), 117–122.CrossRefGoogle Scholar