PACKING ODD PATHS

Let s, t be vertices of a graph G, and let each edge e have a ''capaci ty'' c(e) is an element of R(+). We prove a conjecture of Cook and Seb o that for every k is an element of R(+), the following two statements are equivalent: (i) there is a ''fractional packing'' of value k of t he odd length s-t paths, so that no edge is used more than its capacit y; (ii) for every subgraph H of G with s, t is an element of V(H) in w hich there is no odd s-t path, [GRAPHICS] (C) 1994 Academic Press, Inc .