Nowhere-zero integral chains and flows in bidirected graphs (Q1088883)

The paper presents a general result on nowhere-zero integral chain groups, and special results on flows in bidirected graphs. It is shown that every 4-connected bidirected graph which has at least an unbalanced circuit and a nowhere-zero flow can be provided with a nowhere-zero integral flow with absolute values less than 18. A similar result is obtained for 3-connected and balanced triangle free bidirected graphs. This improves Bouchet's 216-flow theorem for these classes of graphs, and proves his 6-flow conjecture for a class of 3-connected graphs.