Optimal Packings of Hamilton Cycles in Graphs of High Minimum Degree

DANIELA KÜHN, JOHN LAPINSKAS, DERYK OSTHUS
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
more » ... infinitely many values of n and δ. We also extend our results to graphs G of minimum degree δ ≥ n/2, unless G is close to the extremal constructions for Dirac's theorem. Our proof relies on a recent and very general result of Kühn and Osthus on Hamilton decomposition of robustly expanding regular graphs.
doi:10.1017/s0963548312000569 fatcat:74cvhk3lq5fznechirr24pzlje