PIMS - SFU Discrete Mathematics Seminar: Kathryn Nurse

I will present a work in progress. In 1954, Tutte proved flow-colouring duality and made a conjecture that every graph without a cut-edge has a nowhere-zero 5-flow. A parallel conjecture to this, but for signed graphs is Bouchet's conjecture (1983) that every signed graph without the obvious obstruction has a nowhere-zero 6-flow. We have been able to show that Bouchet's conjecture holds for 3-connected graphs when 6 is replaced with 8. This is joint with Matt DeVos and Robert Šámal.