Geodesic
Signed cycle double covers
The electronic journal of combinatorics, Tome 25 (2018) no. 4
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The cycle double cover conjecture states that every bridgeless graph has a collection of cycles which together cover every edge of the graph exactly twice. A signed graph is a graph with each edge assigned by a positive or a negative sign. In this article, we prove a weak version of this conjecture that is the existence of a signed cycle double cover for all bridgeless graphs. We also show the relationships of the signed cycle double cover and other famous conjectures such as the Tutte flow conjectures and the shortest cycle cover conjecture etc.
DOI : 10.37236/6760
Classification : 05C21, 05C22, 05C38, 05C70
Mots-clés : cycle cover, even graph, flow, signed graph 
@article{10_37236_6760,
     author = {Lingsheng Shi and Zhang Zhang},
     title = {Signed cycle double covers},
     journal = {The electronic journal of combinatorics},
     year = {2018},
     volume = {25},
     number = {4},
     doi = {10.37236/6760},
     zbl = {1409.05097},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/6760/}
}
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Lingsheng Shi; Zhang Zhang. Signed cycle double covers. The electronic journal of combinatorics, Tome 25 (2018) no. 4. doi: 10.37236/6760

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