Regular Factors Containing a Given Hamiltonian Cycle
Let k ≥ 1 be an integer and let G be a graph having a sufficiently large order n. Suppose that kn is even, the minimum degree of G is at least k + 2, and the degree sum of each pair of nonadjacent vertices in G is at least n + α, where α = 3 for odd k and α = 4 for even k. Then G has a k – factor (i.e. a k – regular spanning subgraph) which is edge-disjoint from a given Hamiltonian cycle. The lower bound on the degree condition is sharp. As a consequence, we have an Ore-type condition for graphs to have a k – factor containing a given Hamiltonian cycle.
KeywordsMinimum Degree Hamiltonian Cycle Disjoint Subset Large Order Span Subgraph
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