Geodesic
The dimension of the negative cycle vectors of a signed graph
Ars mathematica contemporanea, Tome 16 (2019) no. 2, pp. 625-639 Cet article a éte moissonné depuis la source Ars Mathematica Contemporanea website

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A signed graph is a graph Γ with edges labeled “+” and “−”. The sign of a cycle is the product of its edge signs. Let SpecC(Γ) denote the list of lengths of cycles in Γ. We equip each signed graph with a vector whose entries are the numbers of negative k-cycles for k ∈ SpecC(Γ). These vectors generate a subspace of ℝ|SpecC(Γ)|. Using matchings with a strong permutability property, we provide lower bounds on the dimension of this space; in particular, we show for complete graphs, complete bipartite graphs, and a few other graphs that this space is all of ℝ|SpecC(Γ)|.
DOI : 10.26493/1855-3974.1605.43f
Keywords: Signed graph, negative cycle vector, permutable matching 
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Alex Schaefer; Thomas Zaslavsky. The dimension of the negative cycle vectors of a signed graph. Ars mathematica contemporanea, Tome 16 (2019) no. 2, pp. 625-639. doi: 10.26493/1855-3974.1605.43f

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