2-Reducible Two Paths and an Edge Constructing a Path in (2k + 1)-Edge-Connected Graphs

摘要

Let k ≥ 5 be an odd integer and G = (V(G), E(G)) be a k-edge-connected graph. For denotes the number of edges between X and V(G) − X. We here prove that if is an edge between s ₁ and , and e(Y) ≥ k + 1 for each with , then there exist paths P ₁ and P ₂ such that P _i joins s _i and (i = 1, 2) and is (k − 2)-edge-connected, and in fact we give a generalization of this result.