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arXiv · 1407.5268

Characteristic flows on signed graphs and short circuit covers

Edita Macajova·Martin Skoviera
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Abstract

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 $2(k-1)|E(G)|$.

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Edita Macajova, Martin Skoviera. 2014-07-20. Characteristic flows on signed graphs and short circuit covers. https://arxiv.org/abs/1407.5268

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