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Optimal Packings of Hamilton Cycles in Graphs of High Minimum Degree
2012
Combinatorics, probability & computing
We study the number of edge-disjoint Hamilton cycles one can guarantee in a sufficiently large graph G on n vertices with minimum degree δ = (1/2+α)n. For any constant α > 0, we give an optimal answer in the following sense: let reg even (n, δ) denote the degree of the largest even-regular spanning subgraph one can guarantee in a graph on n vertices with minimum degree δ. Then the number of edge-disjoint Hamilton cycles we find equals reg even (n, δ)/2. The value of reg even (n, δ) is known for
doi:10.1017/s0963548312000569
fatcat:74cvhk3lq5fznechirr24pzlje