Résumé | A signed graph is a graph in which every edge is labelled with a sign, +
or -. In the talk we introduce flows on signed graphs as a natural
analogue of flows on unsigned (that is, all-positive) graphs, based on the
use of bidirected rather than directed edges. After giving a brief survey
of known results about nowhere-zero flows on signed graphs we concentrate
on flows on signed eulerian graphs. We show that every signed eulerian
graph that has a nowhere-zero flow has a nowhere-zero 4-flow. This
indicates a significant difference from the unsigned case where every
eulerian graph is known to have a nowhere-zero 2-flow. We also
characterise those signed eulerian graphs whose flow number equals 2, 3,
and 4, respectively.
This is a joint work with Edita Macajova. |