{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T06:54:30Z","timestamp":1767855270565,"version":"3.49.0"},"reference-count":18,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Inter. Net."],"published-print":{"date-parts":[[2009,9]]},"abstract":"<jats:p> A bipartite graph G is hamiltonian laceable if there is a hamiltonian path between any two vertices of G from distinct vertex bipartite sets. A bipartite graph G is k-edge fault-tolerant hamiltonian laceable if G - F is hamiltonian laceable for every F \u2286 E(G) with |F| \u2264 k. A graph G is k-edge fault-tolerant conditional hamiltonian if G - F is hamiltonian for every F \u2286 E(G) with |F| \u2264 k and \u03b4(G - F) \u2265 2. Let G<jats:sub>0<\/jats:sub> = (V<jats:sub>0<\/jats:sub>, E<jats:sub>0<\/jats:sub>) and G<jats:sub>1<\/jats:sub> = (V<jats:sub>1<\/jats:sub>, E<jats:sub>1<\/jats:sub>) be two disjoint graphs with |V<jats:sub>0<\/jats:sub>| = |V<jats:sub>1<\/jats:sub>|. Let E<jats:sub>r<\/jats:sub> = {(v,\u0278(v)) | v \u03f5 V<jats:sub>0<\/jats:sub>,\u0278(v) \u03f5 V<jats:sub>1<\/jats:sub>, and \u0278: V<jats:sub>0<\/jats:sub> \u2192 V<jats:sub>1<\/jats:sub> is a bijection}. Let G = G<jats:sub>0<\/jats:sub> \u2295 G<jats:sub>1<\/jats:sub> = (V<jats:sub>0<\/jats:sub> \u22c3 V<jats:sub>1<\/jats:sub>, E<jats:sub>0<\/jats:sub> \u22c3 E<jats:sub>1<\/jats:sub> \u22c3 E<jats:sub>r<\/jats:sub>). The set of n-dimensional hypercube-like graphH<jats:sub>n<\/jats:sub> is defined recursively as (a) H<jats:sub>1<\/jats:sub> = K<jats:sub>2<\/jats:sub>, K<jats:sub>2<\/jats:sub> is the complete graph with two vertices, and (b) if G<jats:sub>0<\/jats:sub> and G<jats:sub>1<\/jats:sub> are in H<jats:sub>n<\/jats:sub>, then G = G<jats:sub>0<\/jats:sub> \u2295 G<jats:sub>1<\/jats:sub> is in H<jats:sub>n+1<\/jats:sub>. Let B<jats:sub>n<\/jats:sub> be the set of graphs G where G is bipartite and G \u03f5 H<jats:sub>n<\/jats:sub>. In this paper, we show that every graph in B<jats:sub>n<\/jats:sub> is (n - 2)-edge fault-tolerant hamiltonian laceable if n \u2265 2 and every graph in B<jats:sub>n<\/jats:sub> is (2n - 5)-edge fault-tolerant conditional hamiltonian if n \u2265 3. <\/jats:p>","DOI":"10.1142\/s0219265909002558","type":"journal-article","created":{"date-parts":[[2009,9,23]],"date-time":"2009-09-23T15:33:52Z","timestamp":1253720032000},"page":"243-251","source":"Crossref","is-referenced-by-count":7,"title":["FAULT-TOLERANT HAMILTONIAN LACEABILITY AND FAULT-TOLERANT CONDITIONAL HAMILTONIAN FOR BIPARTITE HYPERCUBE-LIKE NETWORKS"],"prefix":"10.1142","volume":"10","author":[{"given":"CHENG-KUAN","family":"LIN","sequence":"first","affiliation":[{"name":"Department of Computer Science, National Chiao Tung University, Hsinchu, Taiwan 30010, R.O.C."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"TUNG-YANG","family":"HO","sequence":"additional","affiliation":[{"name":"Department of Information Management, Ta Hwa Institute of Technology, Hsinchu, Taiwan 30740, R.O.C."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JIMMY J. M.","family":"TAN","sequence":"additional","affiliation":[{"name":"Department of Computer Science, National Chiao Tung University, Hsinchu, Taiwan 30010, R.O.C."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"LIH-HSING","family":"HSU","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Information Engineering, Providence University, Taichung, Taiwan 43301, R.O.C."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,4,30]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/0743-7315(91)90113-N"},{"key":"rf2","volume-title":"Graph theory with applications","author":"Bondy J. 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