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Adjacent vertices fault tolerant hamiltonian laceability of hypercube graphs
 Proceedings of the 22nd Workshop on Combinatorial Mathematics and Computation Theory
, 2005
"... Let Sn be an ndimensional Star graph. In this paper, we show that Sn − F is Hamiltonian laceable where F is the set of f ≤ (n − 4) pairs of adjacent faulty vertices, Sn − F is Hamiltonian where F is the set of f ≤ (n − 3) pairs of adjacent faulty vertices. We also show that Sn − F is hyperHamilton ..."
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Let Sn be an ndimensional Star graph. In this paper, we show that Sn − F is Hamiltonian laceable where F is the set of f ≤ (n − 4) pairs of adjacent faulty vertices, Sn − F is Hamiltonian where F is the set of f ≤ (n − 3) pairs of adjacent faulty vertices. We also show that Sn − F is hyperHamiltonian
Adjacent vertices faulttolerance for bipancyclicity of hypercube
 THE 25TH WORKSHOP ON COMBINATORIAL MATHEMATICS AND COMPUTATION THEORY
, 2008
"... A bipartite graph G =(V,E) is bipancyclic if it contains the cycles of every even length from 4 to V . Let Fa be the set of fa pairs of adjacent vertices and Fe be the set of fe faulty edges in the ndimensional hypercube Qn. In this paper, we will show that Qn − Fa − Fe is bipancyclic for fa + fe ..."
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A bipartite graph G =(V,E) is bipancyclic if it contains the cycles of every even length from 4 to V . Let Fa be the set of fa pairs of adjacent vertices and Fe be the set of fe faulty edges in the ndimensional hypercube Qn. In this paper, we will show that Qn − Fa − Fe is bipancyclic for fa
Adjacent Vertices Faulttolerance Fanability of Hypercube
, 2006
"... In this paper, we introduce the concepts of fault tolerant fanability. We show that the ndimensional hypercube Qn are fadjacent and l edges fault tolerant (n − f − l) ∗fanable for n ≥ 3, f + l ≤ n − 2 and l ≥ 1. ..."
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In this paper, we introduce the concepts of fault tolerant fanability. We show that the ndimensional hypercube Qn are fadjacent and l edges fault tolerant (n − f − l) ∗fanable for n ≥ 3, f + l ≤ n − 2 and l ≥ 1.
On the Enhanced Hyperhamiltonian Laceability of
"... Abstract — A bipartite graph is hamiltonian laceable if there exists a hamiltonian path between any two vertices that are in different partite sets. A hamiltonian laceable graph G is said to be hyperhamiltonian laceable if, for any vertex v of G, there exists a hamiltonian path of G−{v} joining any ..."
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any two vertices that are located in the same partite set different from that of v. In this paper, we further improve the hyperhamiltonian laceability of hypercubes by showing that, for any two vertices x, y from one partite set of Qn, n ≥ 4, and any vertex w from the other partite set, there exists
Edgepancyclicity and Hamiltonian laceability of the balanced hypercubes
, 2007
"... The balanced hypercube BHn is a variant of the hypercube Qn. Huang and Wu proved that BHn has better properties than Qn with the same number of links and processors. In particularly, they showed that there exists a cycle of length 2 l in BH n for all l, 26 l 6 2n. In this paper, we improve this resu ..."
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Cited by 2 (0 self)
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this result by showing that BH n is edgepancyclic, which means that for arbitrary edge e, there exists a cycle of even length from 4 to 2 2n containing e in BHn. We also show that the balanced hypercubes are Hamiltonian laceable.
HAMILTONIAN LACEABILITY OF HYPERCUBES WITH FAULTS OF CHARGE ONE
"... ABSTRACT. In 2007, in their paper Path coverings with prescribed ends in faulty hypercubes, N. Castañeda and I. Gotchev formulated the following conjecture: Let n and k be positive integers with n ≥ k + 3 and F be a set of k even (odd) and k + 1 odd (even) vertices in the binary hypercube Qn. If u ..."
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Cited by 3 (3 self)
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ABSTRACT. In 2007, in their paper Path coverings with prescribed ends in faulty hypercubes, N. Castañeda and I. Gotchev formulated the following conjecture: Let n and k be positive integers with n ≥ k + 3 and F be a set of k even (odd) and k + 1 odd (even) vertices in the binary hypercube Qn
Paired 2Disjoint Path Covers and Strongly Hamiltonian Laceability of Bipartite HypercubeLike Graphs
, 2013
"... A paired manytomany kdisjoint path cover (paired kDPC for short) of a graph is a set of k vertexdisjoint paths joining k distinct sourcesink pairs that altogether cover every vertex of the graph. We consider the problem of constructing paired 2DPC’s in an mdimensional bipartite HLgraph, Xm, ..."
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. Furthermore, every Xm, m ≥ 4, has a paired 2DPC in which the two paths have the same length if each sourcesink pair is balanced. Using 2DPC properties, we show that every Xm, m ≥ 3, with either at most m − 2 faulty edges or one faulty vertex and at most m − 3 faulty edges is strongly Hamiltonianlaceable.
Adjacent Vertices FaultTolerance Bifanability of Hypercube with the Same Color Sources
 THE 27TH WORKSHOP ON COMBINATORIAL MATHEMATICS AND COMPUTATION THEORY
"... Let Qn = (Vb ∪ Vw, E) be the ndimensional hypercube. Let Fa be the set of fa pairs of adjacently faulty vertices. Let s1, t 2 1, · · · , t k1 1, s2, t 2 2, · · · , t k2 2 ∈ Vi, t 1 1, t 1 2 ∈ Vj be arbitrary faultfree vertices of Qn for {i, j} = {b, w}. In this paper, we construct the spann ..."
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Let Qn = (Vb ∪ Vw, E) be the ndimensional hypercube. Let Fa be the set of fa pairs of adjacently faulty vertices. Let s1, t 2 1, · · · , t k1 1, s2, t 2 2, · · · , t k2 2 ∈ Vi, t 1 1, t 1 2 ∈ Vj be arbitrary faultfree vertices of Qn for {i, j} = {b, w}. In this paper, we construct
The Longest Ring Embedding in Faulty Hypercube
 PROCEEDINGS OF THE 23RD WORKSHOP ON COMBINATORIAL MATHEMATICS AND COMPUTATIONAL THEORY
, 2006
"... In this paper, we show that the adjacency fault tolerance for property 2H of hypercube. We also show that the adjacency fault tolerance for Hamiltonian laceability of hypercube. Applying these results, we can construct the faultfree cycle with length 2 n − 2  Fv  +4 in Qn − Fv where Fv is the fau ..."
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Cited by 4 (3 self)
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In this paper, we show that the adjacency fault tolerance for property 2H of hypercube. We also show that the adjacency fault tolerance for Hamiltonian laceability of hypercube. Applying these results, we can construct the faultfree cycle with length 2 n − 2  Fv  +4 in Qn − Fv where Fv
Results 1  10
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678