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Shorter signed circuit covers of graphs
Tomáš Kaiser, Robert Lukot'ka, Edita Máčajová +1
A signed circuit is a minimal signed graph (with respect to inclusion) that admits a nowhere-zero flow. We show that each flow-admissible signed graph on edges can be covered b…
A note on counting flows in signed graphs
Matt DeVos, Edita Rollová, Robert Šámal
Tutte initiated the study of nowhere-zero flows and proved the following fundamental theorem: For every graph there is a polynomial so that for every abelian group of o…
3-Flows with Large Support
Matt DeVos, Jessica McDonald, Irene Pivotto +2
We prove that every 3-edge-connected graph has a 3-flow with the property that . The graph demonstrates that this $\frac{5}…
A new proof of Seymour's 6-flow theorem
Matt DeVos, Edita Rollová, Robert Šámal
Tutte's famous 5-flow conjecture asserts that every bridgeless graph has a nowhere-zero 5-flow. Seymour proved that every such graph has a nowhere-zero 6-flow. Here we give (two ve…
Nowhere-zero flows in signed series-parallel graphs
Tomáš Kaiser, Edita Rollová
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 gr…