Nowhere-zero flows in signed series-parallel graphs
Tom\'a\v{s} Kaiser, Edita Rollov\'a
TL;DR
This paper proves Bouchet's conjecture for signed series-parallel graphs, showing that such graphs admit a nowhere-zero 6-flow, which is a significant step in understanding flow properties in signed graphs.
Contribution
The paper establishes Bouchet's conjecture specifically for signed series-parallel graphs, a nontrivial case not covered by previous results.
Findings
Bouchet's conjecture holds for all signed series-parallel graphs.
The result is tight for infinitely many graphs.
The proof advances understanding of flow properties in signed graphs.
Abstract
Bouchet conjectured in 1983 that each signed graph that admits a nowhere-zero flow has a nowhere-zero 6-flow. We prove that the conjecture is true for all signed series-parallel graphs. Unlike the unsigned case, the restriction to series-parallel graphs is nontrivial; in fact, the result is tight for infinitely many graphs.
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