1-Vertex-Hamiltonian-Laceability of Hypercubes with Maximal Edge Faults

• Main Authors: Zhe-Nan Guo, 郭哲男
• Other Authors: Sun-Yuan Hsieh
• Format: Others
• Language: en_US
• Published: 2004
• Online Access: http://ndltd.ncl.edu.tw/handle/47276269802483134455

碩士 === 國立成功大學 === 資訊工程學系碩博士班 === 92 === Suppose that G = (V_0 union V_1,E) is a bipartite graph with two partite sets V_0 and V_1 of equal size. Let x and y be two arbitrary distinct vertices and let w be another vertex different from x and y. G is said to be 1-vertex-Hamiltonian-laceable if G-w satisfies the following three properties. P1: There is a (lV_0l + lV_1l - 2)-length path between x and y, where x and y are in the same partite set and w is in the other partite set; P2: There is a (lV_0l + lV_1l - 3)-length path between x and y, where x and y are in different partite sets and w is in any partite set; P3: There is a (lV_0l + lV_1l - 4)-length path between x and y, where x,y,w are in the same partite set. Let Fe be the set of faulty edges of an n-dimensional hypercube Qn. In this paper, we show that Qn - Fe (the graph obtained by deleting all edges of Fe from Qn) remains 1-vertex-Hamiltonian-laceable when lFel less than n-3.