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A theorem on connected graphs in which every edge belongs to a 1-factor

Published online by Cambridge University Press:  09 April 2009

Charles H. C. Little
Charles H. C. Little
Affiliation:
Department of Mathematics and Computer ScienceRoyal Melbourne Institute of Technology, Victoria, 3000, Australia
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In this paper, we consider factor covered graphs, which are defined basically as connected graphs in which every edge belongs to a 1-factor. The main theorem is that for any two edges e and e′ of a factor covered graph, there is a cycle C passing through e and e′ such that the edge set of C is the symmetric difference of two 1-factors.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 18 , Issue 4 , December 1974 , pp. 450 - 452
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Behzad, M. and Chartrand, G.; Introduction to the Theory of Graphs (Allyn & Bacon, Boston, 1971).Google Scholar