Combinatorics, Probability and Computing
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
Digraphs: Theory, Algorithms and Applications
Digraphs: Theory, Algorithms and Applications
Hamiltonian degree sequences in digraphs
Journal of Combinatorial Theory Series B
A survey on Hamilton cycles in directed graphs
European Journal of Combinatorics
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We show that for each $\beta 0$, every digraph $G$ of sufficiently large order $n$ whose outdegree and indegree sequences $d_1^+ \leq \cdots \leq d_n^+$ and $d_1^- \leq \cdots \leq d_n^-$ satisfy $d_i^+, d_i^- \geq \min{\{i + \beta n, n/2\}}$ is Hamiltonian. In fact, we can weaken these assumptions to (i) $d_i^+ \geq \min{\{i + \beta n, n/2\}}$ or $d^-_{n - i - \beta n} \geq n-i$, (ii) $d_i^- \geq \min{\{i + \beta n, n/2\}}$ or $d^+_{n - i - \beta n} \geq n-i$, and still deduce that $G$ is Hamiltonian. This provides an approximate version of a conjecture of Nash-Williams from 1975 and improves a previous result of Kühn, Osthus, and Treglown.