Geodesic
Characteristic flows on signed graphs and short circuit covers
The electronic journal of combinatorics, Tome 23 (2016) no. 3
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We generalise to signed graphs a classical result of Tutte [Canad. J. Math. 8 (1956), 13—28] stating that every integer flow can be expressed as a sum of characteristic flows of circuits. In our generalisation, the rôle of circuits is taken over by signed circuits of a signed graph which occur in two types — either balanced circuits or pairs of disjoint unbalanced circuits connected with a path intersecting them only at its ends. As an application of this result we show that a signed graph $G$ admitting a nowhere-zero $k$-flow has a covering with signed circuits of total length at most $2(k-1)|E(G)|$.
DOI : 10.37236/4872
Classification : 05C21, 05C22
Mots-clés : signed graph, flows 
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     author = {Edita M\'a\v{c}ajov\'a and Martin \v{S}koviera},
     title = {Characteristic flows on signed graphs and short circuit covers},
     journal = {The electronic journal of combinatorics},
     year = {2016},
     volume = {23},
     number = {3},
     doi = {10.37236/4872},
     zbl = {1344.05066},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/4872/}
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Edita Máčajová; Martin Škoviera. Characteristic flows on signed graphs and short circuit covers. The electronic journal of combinatorics, Tome 23 (2016) no. 3. doi: 10.37236/4872

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