The algorithmic aspects of the regularity lemma
Journal of Algorithms
Basic graph theory: paths and circuits
Handbook of combinatorics (vol. 1)
Edge coloring regular graphs of high degree
Proceedings of an international symposium on Graphs and combinatorics
Hamiltonian decomposition of complete regular multipartite digraphs
Discrete Mathematics
Journal of Combinatorial Theory Series B
Random regular graphs of high degree
Random Structures & Algorithms
Algorithms with large domination ratio
Journal of Algorithms
Testing subgraphs in directed graphs
Journal of Computer and System Sciences - Special issue: STOC 2003
On packing Hamilton cycles in ε-regular graphs
Journal of Combinatorial Theory Series B
A dirac-type result on hamilton cycles in oriented graphs
Combinatorics, Probability and Computing
Hamiltonian degree sequences in digraphs
Journal of Combinatorial Theory Series B
A survey on Hamilton cycles in directed graphs
European Journal of Combinatorics
Approximate Hamilton decompositions of random graphs
Random Structures & Algorithms
TSP tour domination and Hamilton cycle decompositions of regular digraphs
Operations Research Letters
Edge-disjoint Hamilton cycles in graphs
Journal of Combinatorial Theory Series B
Embedding spanning bipartite graphs of small bandwidth
Combinatorics, Probability and Computing
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In a recent paper, we showed that every sufficiently large regular digraph G on n vertices whose degree is linear in n and which is a robust outexpander has a decomposition into edge-disjoint Hamilton cycles. The main consequence of this theorem is that every regular tournament on n vertices can be decomposed into (n-1)/2 edge-disjoint Hamilton cycles, whenever n is sufficiently large. This verified a conjecture of Kelly from 1968. In this paper, we derive a number of further consequences of our result on robust outexpanders, the main ones are the following:(i)an undirected analogue of our result on robust outexpanders; (ii)best possible bounds on the size of an optimal packing of edge-disjoint Hamilton cycles in a graph of minimum degree @d for a large range of values for @d. (iii)a similar result for digraphs of given minimum semidegree; (iv)an approximate version of a conjecture of Nash-Williams on Hamilton decompositions of dense regular graphs; (v)a verification of the 'very dense' case of a conjecture of Frieze and Krivelevich on packing edge-disjoint Hamilton cycles in random graphs; (vi)a proof of a conjecture of Erdos on the size of an optimal packing of edge-disjoint Hamilton cycles in a random tournament.