MENGER-TYPE THEOREMS WITH RESTRICTIONS ON PATH LENGTHS

If the paths of length less-than-or-equal-to s, joining two non-adjace nt vertices u, v of a graph cannot be destroyed by deleting less than t vertices, then there are at least t internally vertex-disjoint paths joining u and v, each having length less than t + s - 2/s - 2) + (t s - 3/s - 2). Some constructions show that using paths of length at l east right perpendicular s/t - 1 left perpendicular(t) might be necess ary.