Skip to Main Content
Assume that u and v are any two distinct vertices of different partite sets of Sn with n ≥ 5. We prove that there are (n - 1) internally disjoint paths P1, P2, ..., Pn-i joining u to v such that ∪n = 1i = 2 Pi spans Sn and l(Pi) ≤ (n - 1)! + 2(n - 2)! + 2(n - 3)! + 1 = n!/(n - 2) + 1. We also prove that there are two internally disjoint paths Q1 and Q2 joining u to v such that Q1 ∪ Q2 spans Sn and l(Qi) ≤ n!/2 + l for i = 1,2.