Characteristic Flows on Signed Graphs and Short Circuit Covers
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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 $2(k-1)|E(G)|$.
2020 ◽
Vol 92
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pp. 20901
2004 ◽
Vol 286
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pp. G814-G821
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Vol 303
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pp. C936-C946
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1999 ◽
Vol 276
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pp. G28-G36
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Vol 45
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pp. 3213
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