A theorem on connected graphs in which every edge belongs to a 1-factor
- 1 December 1974
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society
- Vol. 18 (4) , 450-452
- https://doi.org/10.1017/s144678870002913x
Abstract
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.Keywords
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