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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
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Abstract

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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

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