Classification of Conformally Indecomposable Integral Flows on Signed Graphs
نویسندگان
چکیده
A conformally indecomposable flow f on a signed graph Σ is a nonzero integral flow that cannot be decomposed into f = f1 + f2, where f1, f2 are nonzero integral flows having the same sign (both ≥ 0 or both ≤ 0) at every edge. This paper is to classify at integer scale conformally indecomposable flows into characteristic vectors of Eulerian cycle-trees — a class of signed graphs having a kind of tree structure in which all cycles can be viewed as vertices of a tree. Moreover, each conformally indecomposable flow other than signed-graphic circuit flows can be further decomposed conformally at half-integer scale into a sum of certain signed-graphic circuit flows. The variety of conformally indecomposable flows of signed graphs is much richer than that of ordinary unsigned graphs.
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