EXTENSIONS OF FLOW THEOREMS

As an extension of Seymour's 6-flow theorem, we prove that every 2-edg e-connected graph has a set of vertex-disjoint circuits and a 3-flow f such that f(e) = 0 only if e is an edge in one of the circuits. An ex tension of Jaeger's 8-flow theorem, together with applications to the short cycle cover problem, is also presented. It is shown that the edg es of a 2-edge-connected graph G can be covered by cycles whose total length is at most \E(G)\ + r/r+1(\V(G)\-1), where r is the minimum len gth of an even circuit (of G) of length at least 10 (r = infinity, if there is no such circuit). (C) 1997 Academic Press.