Symmetric property and edge-disjoint Hamiltonian cycles of the spined cube

Random partitions and edge-disjoint Hamiltonian cycles

Nash-Williams [21] proved that every graph with n vertices and minimum degree n/2 has at least b5n/224c edge-disjoint Hamiltonian cycles. In [20], he raised the question of determining the maximum number of edge-disjoint Hamiltonian cycles, showing an upper bound of b(n+ 4)/8c. Let α(δ, n) = (δ + √ 2δn− n2)/2. Christofides, Kühn, and Osthus [7] proved that for every > 0, every graph G on a suff...

The property of edge-disjoint Hamiltonian cycles in transposition networks and hypercube-like networks

The presence of edge-disjoint Hamiltonian cycles provides an advantage when implementing algorithms that require a ring structure by allowing message traffic to be spread evenly across the network. Edge-disjoint Hamiltonian cycles also provide the edge-fault tolerant hamiltonicity of an interconnection network. In this paper, we first study the property of edge-disjoint Hamiltonian cycles in tr...

The Problem of Finding Two Edge-Disjoint Hamiltonian Cycles

Embedding Two Edge-Disjoint Hamiltonian Cycles and Two Equal Node-Disjoint Cycles into Twisted Cubes

The presence of edge-disjoint Hamiltonian cycles provides an advantage when implementing algorithms that require a ring structure by allowing message traffic to be spread evenly across the network. Edge-disjoint Hamiltonian cycles also provide the edge-fault tolerant Hamiltonicity of an interconnection network. Two node-disjoint cycles in a network are called equal if the number of nodes in the...

Edge-disjoint Hamiltonian Paths and Cycles in Tournaments

We describe sufficient conditions for the existence of Hamiltonian paths in oriented graphs and use these to provide a complete description of the tournaments with no two edge-disjoint Hamiltonian paths. We prove that tournaments with small irregularity have many edge-disjoint Hamiltonian cycles in support of Kelly's conjecture.