기초과학연구원 이산수학그룹
On September 22, 2025, Rong Luo from West Virginia University gave a talk at the Discrete Math Seminar on nowhere-zero flows on signed graphs. His talk was titled “Modulo flows and Integer flows of signed graphs“.
Nowhere-zero flows of unsigned graphs were introduced by Tutte in 1954 as a dual problem to vertex-coloring of (unsigned) planar graphs. The definition of nowhere-zero flows on signed graphs naturally comes from the study of embeddings of graphs in non-orientable surfaces, where nowhere-zero flows emerge as the dual notion to local tensions. Nowhere-zero flows in signed graphs were introduced by Edmonds and Johnson in 1970 for expressing algorithms on matchings, but systematically studied first by Bouchet in 1983. Bouchet also stated a conjecture which occupies a central place in the area of signed graphs: Every flow-admissible signed graph admits a nowhere-zero 6-flow. There is a significant difference in the flows of signed graphs and unsigned graphs. In this talk I will talk about the progress on the development of the flow theory of signed graphs.